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Expresiones idénticas
(x*x*x+ tres)^(- dos)*(sin(dos *x)*(seis -x*x*x)+x*(dos *cos(dos *x)*(x*x*x+ doce)+x*(seis *cos(dos *x)*x*x- seis *x/(x*x*x+ tres)*(dos *x*cos(dos *x)*(x*x*x+ tres)+sin(dos *x)*(seis -x*x*x))+sin(dos *x)*(- cuatro *(x*x*x+ tres)- tres *x))))
(x multiplicar por x multiplicar por x más 3) en el grado ( menos 2) multiplicar por ( seno de (2 multiplicar por x) multiplicar por (6 menos x multiplicar por x multiplicar por x) más x multiplicar por (2 multiplicar por coseno de (2 multiplicar por x) multiplicar por (x multiplicar por x multiplicar por x más 12) más x multiplicar por (6 multiplicar por coseno de (2 multiplicar por x) multiplicar por x multiplicar por x menos 6 multiplicar por x dividir por (x multiplicar por x multiplicar por x más 3) multiplicar por (2 multiplicar por x multiplicar por coseno de (2 multiplicar por x) multiplicar por (x multiplicar por x multiplicar por x más 3) más seno de (2 multiplicar por x) multiplicar por (6 menos x multiplicar por x multiplicar por x)) más seno de (2 multiplicar por x) multiplicar por ( menos 4 multiplicar por (x multiplicar por x multiplicar por x más 3) menos 3 multiplicar por x))))
(x multiplicar por x multiplicar por x más tres) en el grado ( menos dos) multiplicar por ( seno de (dos multiplicar por x) multiplicar por (seis menos x multiplicar por x multiplicar por x) más x multiplicar por (dos multiplicar por coseno de (dos multiplicar por x) multiplicar por (x multiplicar por x multiplicar por x más doce) más x multiplicar por (seis multiplicar por coseno de (dos multiplicar por x) multiplicar por x multiplicar por x menos seis multiplicar por x dividir por (x multiplicar por x multiplicar por x más tres) multiplicar por (dos multiplicar por x multiplicar por coseno de (dos multiplicar por x) multiplicar por (x multiplicar por x multiplicar por x más tres) más seno de (dos multiplicar por x) multiplicar por (seis menos x multiplicar por x multiplicar por x)) más seno de (dos multiplicar por x) multiplicar por ( menos cuatro multiplicar por (x multiplicar por x multiplicar por x más tres) menos tres multiplicar por x))))
(x*x*x+3)(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
x*x*x+3-2*sin2*x*6-x*x*x+x*2*cos2*x*x*x*x+12+x*6*cos2*x*x*x-6*x/x*x*x+3*2*x*cos2*x*x*x*x+3+sin2*x*6-x*x*x+sin2*x*-4*x*x*x+3-3*x
(xxx+3)^(-2)(sin(2x)(6-xxx)+x(2cos(2x)(xxx+12)+x(6cos(2x)xx-6x/(xxx+3)(2xcos(2x)(xxx+3)+sin(2x)(6-xxx))+sin(2x)(-4(xxx+3)-3x))))
(xxx+3)(-2)(sin(2x)(6-xxx)+x(2cos(2x)(xxx+12)+x(6cos(2x)xx-6x/(xxx+3)(2xcos(2x)(xxx+3)+sin(2x)(6-xxx))+sin(2x)(-4(xxx+3)-3x))))
xxx+3-2sin2x6-xxx+x2cos2xxxx+12+x6cos2xxx-6x/xxx+32xcos2xxxx+3+sin2x6-xxx+sin2x-4xxx+3-3x
xxx+3^-2sin2x6-xxx+x2cos2xxxx+12+x6cos2xxx-6x/xxx+32xcos2xxxx+3+sin2x6-xxx+sin2x-4xxx+3-3x
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x dividir por (x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
Expresiones semejantes
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6+x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)+3*x))))
(x*x*x+3)^(2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x-3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)-sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x+6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x-3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x-12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)-x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6+x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))-sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x-3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)-x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x-3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))
(x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(4*(x*x*x+3)-3*x))))
Expresiones con funciones
Seno sin
sin^-1(x)
sin²(x)
sin(x)^(23)
sin(2*y)
sin(x)^(cos(x))
Coseno cos
cos(3)^(2)*x
cos2
cos(5-3*x)
cos(x)^(100)
cos/sin
Coseno cos
cos(3)^(2)*x
cos2
cos(5-3*x)
cos(x)^(100)
cos/sin
Coseno cos
cos(3)^(2)*x
cos2
cos(5-3*x)
cos(x)^(100)
cos/sin
Seno sin
sin^-1(x)
sin²(x)
sin(x)^(23)
sin(2*y)
sin(x)^(cos(x))
Seno sin
sin^-1(x)
sin²(x)
sin(x)^(23)
sin(2*y)
sin(x)^(cos(x))

Derivada de la función/ (x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))

Derivada de (xxx+3)^(-2)(sin(2x)(6-xxx)+x(2cos(2x)(xxx+12)+x(6cos(2x)xx-6x/(xxx+3)(2xcos(2x)(xxx+3)+sin(2x)(6-xxx))+sin(2x)(-4(xxx+3)-3x))))

Solución

Ha introducido [src]

                         /                            /                    6*x                                                                                       \\
sin(2*x)*(6 - x*x*x) + x*|2*cos(2*x)*(x*x*x + 12) + x*|6*cos(2*x)*x*x - ---------*(2*x*cos(2*x)*(x*x*x + 3) + sin(2*x)*(6 - x*x*x)) + sin(2*x)*(-4*(x*x*x + 3) - 3*x)||
                         \                            \                 x*x*x + 3                                                                                    //
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                                                                                         2                                                                             
                                                                              (x*x*x + 3)

$$\frac{x \left(x \left(\left(- 3 x - 4 \left(x x x + 3\right)\right) \sin{\left(2 x \right)} + \left(x x 6 \cos{\left(2 x \right)} - \frac{6 x}{x x x + 3} \left(2 x \cos{\left(2 x \right)} \left(x x x + 3\right) + \left(- x x x + 6\right) \sin{\left(2 x \right)}\right)\right)\right) + \left(x x x + 12\right) 2 \cos{\left(2 x \right)}\right) + \left(- x x x + 6\right) \sin{\left(2 x \right)}}{\left(x x x + 3\right)^{2}}$$

(sin(2*x)*(6 - x*x*x) + x*((2*cos(2*x))*((x*x)*x + 12) + x*(((6*cos(2*x))*x)*x - (6*x)/((x*x)*x + 3)*(((2*x)*cos(2*x))*((x*x)*x + 3) + sin(2*x)*(6 - x*x*x)) + sin(2*x)*(-4*((x*x)*x + 3) - 3*x))))/((x*x)*x + 3)^2

Solución detallada

Se aplica la regla de la derivada parcial:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x \left(x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right) + \left(6 - x^{3}\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)}$ y $g{\left(x \right)} = \left(x^{3} + 3\right)^{3}$ .

Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
1. diferenciamos $x \left(x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right) + \left(6 - x^{3}\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)}$ miembro por miembro:
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. Según el principio, aplicamos: $x$ tenemos $1$
    $g{\left(x \right)} = x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. diferenciamos $x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}$ miembro por miembro:
      1. Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        $g{\left(x \right)} = 6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        diferenciamos $6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}$ miembro por miembro:
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        $g{\left(x \right)} = 2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        diferenciamos $2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}$ miembro por miembro:
        
        Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = 6 - x^{3}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        diferenciamos $6 - x^{3}$ miembro por miembro:
        
        La derivada de una constante $6$ es igual a cero.
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Entonces, como resultado: $- 3 x^{2}$
        
        Como resultado de: $- 3 x^{2}$
        
        $g{\left(x \right)} = \sin{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        Sustituimos $u = 2 x$ .
        
        La derivada del seno es igual al coseno:
        
        $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
        
        Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} 2 x$ :
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $2$
        
        Como resultado de la secuencia de reglas:
        
        $2 \cos{\left(2 x \right)}$
        
        Como resultado de: $- 3 x^{2} \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)}$
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} h{\left(x \right)} = f{\left(x \right)} g{\left(x \right)} \frac{d}{d x} h{\left(x \right)} + f{\left(x \right)} h{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} h{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        $g{\left(x \right)} = x^{3} + 3$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        diferenciamos $x^{3} + 3$ miembro por miembro:
        
        La derivada de una constante $3$ es igual a cero.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Como resultado de: $3 x^{2}$
        
        $h{\left(x \right)} = \cos{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} h{\left(x \right)}$ :
        
        Sustituimos $u = 2 x$ .
        
        La derivada del coseno es igual a menos el seno:
        
        $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
        
        Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} 2 x$ :
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $2$
        
        Como resultado de la secuencia de reglas:
        
        $- 2 \sin{\left(2 x \right)}$
        
        Como resultado de: $3 x^{3} \cos{\left(2 x \right)} - 2 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + \left(x^{3} + 3\right) \cos{\left(2 x \right)}$
        
        Entonces, como resultado: $6 x^{3} \cos{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}$
        
        Como resultado de: $6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}$
        
        Como resultado de: $2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) + \left(6 - x^{3}\right) \sin{\left(2 x \right)}$
        
        Entonces, como resultado: $- 12 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) - 6 \left(6 - x^{3}\right) \sin{\left(2 x \right)}$
        
        Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} h{\left(x \right)} = f{\left(x \right)} g{\left(x \right)} \frac{d}{d x} h{\left(x \right)} + f{\left(x \right)} h{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} h{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x^{3} + 3$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        diferenciamos $x^{3} + 3$ miembro por miembro:
        
        La derivada de una constante $3$ es igual a cero.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Como resultado de: $3 x^{2}$
        
        $g{\left(x \right)} = - 4 x^{3} - 3 x - 12$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        diferenciamos $- 4 x^{3} - 3 x - 12$ miembro por miembro:
        
        La derivada de una constante $-12$ es igual a cero.
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Entonces, como resultado: $- 12 x^{2}$
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $-3$
        
        Como resultado de: $- 12 x^{2} - 3$
        
        $h{\left(x \right)} = \sin{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} h{\left(x \right)}$ :
        
        Sustituimos $u = 2 x$ .
        
        La derivada del seno es igual al coseno:
        
        $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
        
        Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} 2 x$ :
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $2$
        
        Como resultado de la secuencia de reglas:
        
        $2 \cos{\left(2 x \right)}$
        
        Como resultado de: $3 x^{2} \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)} + \left(- 12 x^{2} - 3\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \cos{\left(2 x \right)}$
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} h{\left(x \right)} = f{\left(x \right)} g{\left(x \right)} \frac{d}{d x} h{\left(x \right)} + f{\left(x \right)} h{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} h{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x^{2}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        Según el principio, aplicamos: $x^{2}$ tenemos $2 x$
        
        $g{\left(x \right)} = x^{3} + 3$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        diferenciamos $x^{3} + 3$ miembro por miembro:
        
        La derivada de una constante $3$ es igual a cero.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Como resultado de: $3 x^{2}$
        
        $h{\left(x \right)} = \cos{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} h{\left(x \right)}$ :
        
        Sustituimos $u = 2 x$ .
        
        La derivada del coseno es igual a menos el seno:
        
        $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
        
        Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} 2 x$ :
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $2$
        
        Como resultado de la secuencia de reglas:
        
        $- 2 \sin{\left(2 x \right)}$
        
        Como resultado de: $3 x^{4} \cos{\left(2 x \right)} - 2 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)}$
        
        Entonces, como resultado: $18 x^{4} \cos{\left(2 x \right)} - 12 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 12 x \left(x^{3} + 3\right) \cos{\left(2 x \right)}$
        
        Como resultado de: $18 x^{4} \cos{\left(2 x \right)} - 12 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 3 x^{2} \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)} - 6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) - 6 \left(6 - x^{3}\right) \sin{\left(2 x \right)} + \left(- 12 x^{2} - 3\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \cos{\left(2 x \right)}$
        
        Como resultado de: $6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + x \left(18 x^{4} \cos{\left(2 x \right)} - 12 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 3 x^{2} \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)} - 6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) - 6 \left(6 - x^{3}\right) \sin{\left(2 x \right)} + \left(- 12 x^{2} - 3\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \cos{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}$
      2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Se aplica la regla de la derivada de una multiplicación:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} h{\left(x \right)} = f{\left(x \right)} g{\left(x \right)} \frac{d}{d x} h{\left(x \right)} + f{\left(x \right)} h{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} h{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x^{3} + 3$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
        
        diferenciamos $x^{3} + 3$ miembro por miembro:
        
        La derivada de una constante $3$ es igual a cero.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Como resultado de: $3 x^{2}$
        
        $g{\left(x \right)} = x^{3} + 12$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
        
        diferenciamos $x^{3} + 12$ miembro por miembro:
        
        La derivada de una constante $12$ es igual a cero.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Como resultado de: $3 x^{2}$
        
        $h{\left(x \right)} = \cos{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} h{\left(x \right)}$ :
        
        Sustituimos $u = 2 x$ .
        
        La derivada del coseno es igual a menos el seno:
        
        $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
        
        Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} 2 x$ :
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $2$
        
        Como resultado de la secuencia de reglas:
        
        $- 2 \sin{\left(2 x \right)}$
        
        Como resultado de: $3 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 3 x^{2} \left(x^{3} + 12\right) \cos{\left(2 x \right)} - 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \sin{\left(2 x \right)}$
        
        Entonces, como resultado: $6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 6 x^{2} \left(x^{3} + 12\right) \cos{\left(2 x \right)} - 4 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \sin{\left(2 x \right)}$
      Como resultado de: $12 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 6 x^{2} \left(x^{3} + 12\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + x \left(18 x^{4} \cos{\left(2 x \right)} - 12 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 3 x^{2} \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)} - 6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) - 6 \left(6 - x^{3}\right) \sin{\left(2 x \right)} + \left(- 12 x^{2} - 3\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \cos{\left(2 x \right)}\right) - 4 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \sin{\left(2 x \right)} + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}$
    Como resultado de: $x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + x \left(12 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 6 x^{2} \left(x^{3} + 12\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + x \left(18 x^{4} \cos{\left(2 x \right)} - 12 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 3 x^{2} \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)} - 6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) - 6 \left(6 - x^{3}\right) \sin{\left(2 x \right)} + \left(- 12 x^{2} - 3\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \cos{\left(2 x \right)}\right) - 4 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \sin{\left(2 x \right)} + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}$
  2. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} h{\left(x \right)} = f{\left(x \right)} g{\left(x \right)} \frac{d}{d x} h{\left(x \right)} + f{\left(x \right)} h{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} h{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x^{3} + 3$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. diferenciamos $x^{3} + 3$ miembro por miembro:
      1. La derivada de una constante $3$ es igual a cero.
      2. Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
      Como resultado de: $3 x^{2}$
    $g{\left(x \right)} = 6 - x^{3}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. diferenciamos $6 - x^{3}$ miembro por miembro:
      1. La derivada de una constante $6$ es igual a cero.
      2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
        
        Entonces, como resultado: $- 3 x^{2}$
      Como resultado de: $- 3 x^{2}$
    $h{\left(x \right)} = \sin{\left(2 x \right)}$ ; calculamos $\frac{d}{d x} h{\left(x \right)}$ :
    1. Sustituimos $u = 2 x$ .
    2. La derivada del seno es igual al coseno:
      
      $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} 2 x$ :
      1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x$ tenemos $1$
        
        Entonces, como resultado: $2$
      Como resultado de la secuencia de reglas:
      
      $2 \cos{\left(2 x \right)}$
    Como resultado de: $3 x^{2} \left(6 - x^{3}\right) \sin{\left(2 x \right)} - 3 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \left(x^{3} + 3\right) \cos{\left(2 x \right)}$
  Como resultado de: $3 x^{2} \left(6 - x^{3}\right) \sin{\left(2 x \right)} - 3 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + x \left(12 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 6 x^{2} \left(x^{3} + 12\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + x \left(18 x^{4} \cos{\left(2 x \right)} - 12 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 3 x^{2} \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)} - 6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) - 6 \left(6 - x^{3}\right) \sin{\left(2 x \right)} + \left(- 12 x^{2} - 3\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \cos{\left(2 x \right)}\right) - 4 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \sin{\left(2 x \right)} + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(6 - x^{3}\right) \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}$
Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
1. Sustituimos $u = x^{3} + 3$ .
2. Según el principio, aplicamos: $u^{3}$ tenemos $3 u^{2}$
3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x^{3} + 3\right)$ :
  1. diferenciamos $x^{3} + 3$ miembro por miembro:
    1. La derivada de una constante $3$ es igual a cero.
    2. Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
    Como resultado de: $3 x^{2}$
  Como resultado de la secuencia de reglas:
  
  $9 x^{2} \left(x^{3} + 3\right)^{2}$
Ahora aplicamos la regla de la derivada de una divesión:

$\frac{- 9 x^{2} \left(x^{3} + 3\right)^{2} \left(x \left(x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right) + \left(6 - x^{3}\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right)^{3} \left(3 x^{2} \left(6 - x^{3}\right) \sin{\left(2 x \right)} - 3 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + x \left(6 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + x \left(12 x^{2} \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 6 x^{2} \left(x^{3} + 12\right) \cos{\left(2 x \right)} - 6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right) + x \left(18 x^{4} \cos{\left(2 x \right)} - 12 x^{2} \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 3 x^{2} \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)} - 6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 4 x \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(6 - x^{3}\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \cos{\left(2 x \right)}\right) - 6 \left(6 - x^{3}\right) \sin{\left(2 x \right)} + \left(- 12 x^{2} - 3\right) \left(x^{3} + 3\right) \sin{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \cos{\left(2 x \right)}\right) - 4 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \sin{\left(2 x \right)} + \left(x^{3} + 3\right) \left(- 4 x^{3} - 3 x - 12\right) \sin{\left(2 x \right)}\right) + 2 \left(6 - x^{3}\right) \left(x^{3} + 3\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right)}{\left(x^{3} + 3\right)^{6}}$
Simplificamos:

$\frac{- 8 x^{11} \cos{\left(2 x \right)} + 12 x^{10} \sin{\left(2 x \right)} + 12 x^{9} \cos{\left(2 x \right)} - 6 x^{8} \sin{\left(2 x \right)} - 72 x^{8} \cos{\left(2 x \right)} - 216 x^{6} \cos{\left(2 x \right)} + 288 x^{5} \sin{\left(2 x \right)} - 216 x^{5} \cos{\left(2 x \right)} - 324 x^{4} \sin{\left(2 x \right)} - 648 x^{3} \cos{\left(2 x \right)} - 540 x^{2} \sin{\left(2 x \right)} - 216 x^{2} \cos{\left(2 x \right)} - 648 x \sin{\left(2 x \right)} + 324 \cos{\left(2 x \right)}}{x^{12} + 12 x^{9} + 54 x^{6} + 108 x^{3} + 81}$

Respuesta:

$\frac{- 8 x^{11} \cos{\left(2 x \right)} + 12 x^{10} \sin{\left(2 x \right)} + 12 x^{9} \cos{\left(2 x \right)} - 6 x^{8} \sin{\left(2 x \right)} - 72 x^{8} \cos{\left(2 x \right)} - 216 x^{6} \cos{\left(2 x \right)} + 288 x^{5} \sin{\left(2 x \right)} - 216 x^{5} \cos{\left(2 x \right)} - 324 x^{4} \sin{\left(2 x \right)} - 648 x^{3} \cos{\left(2 x \right)} - 540 x^{2} \sin{\left(2 x \right)} - 216 x^{2} \cos{\left(2 x \right)} - 648 x \sin{\left(2 x \right)} + 324 \cos{\left(2 x \right)}}{x^{12} + 12 x^{9} + 54 x^{6} + 108 x^{3} + 81}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                                                                                                                       /  /                                                /                  /     2      \\                                                                                                                            /                                             2                                         /   2      \         \\                                                                                                                                                                     \                                                                                                                                                                                                                                                                
  /                    6*x                                                                                       \     |  |                                                |      6       6*x*\- 2*x  - x*x/|                                                     /        2        \                                                6*x*\(2*cos(2*x) - 4*x*sin(2*x))*(x*x*x + 3) - 3*x *sin(2*x) + 2*(6 - x*x*x)*cos(2*x) + 2*x*\2*x  + x*x/*cos(2*x)/|                                                         6*x                                                                                    /   2      \         |                                2                                                                                                                                                                                                                               
x*|6*cos(2*x)*x*x - ---------*(2*x*cos(2*x)*(x*x*x + 3) + sin(2*x)*(6 - x*x*x)) + sin(2*x)*(-4*(x*x*x + 3) - 3*x)| + x*|x*|x*(6*cos(2*x) - 12*x*sin(2*x)) + 6*cos(2*x)*x + |- --------- - ------------------|*(2*x*cos(2*x)*(x*x*x + 3) + sin(2*x)*(6 - x*x*x)) + \-3 - 8*x  - 4*x*x/*sin(2*x) + 2*(-4*(x*x*x + 3) - 3*x)*cos(2*x) - ------------------------------------------------------------------------------------------------------------------| + 6*cos(2*x)*x*x + sin(2*x)*(-4*(x*x*x + 3) - 3*x) - ---------*(2*x*cos(2*x)*(x*x*x + 3) + sin(2*x)*(6 - x*x*x)) - 4*(x*x*x + 12)*sin(2*x) + 2*\2*x  + x*x/*cos(2*x)| + 2*cos(2*x)*(x*x*x + 12) - 3*x *sin(2*x) + 2*(6 - x*x*x)*cos(2*x)   /     2        \ /                         /                            /                    6*x                                                                                       \\\
  \                 x*x*x + 3                                                                                    /     |  |                                                |  x*x*x + 3                 2   |                                                                                                                                                                            x*x*x + 3                                                     |                                                      x*x*x + 3                                                                                                      |                                                                      \- 4*x  - 2*x*x/*|sin(2*x)*(6 - x*x*x) + x*|2*cos(2*x)*(x*x*x + 12) + x*|6*cos(2*x)*x*x - ---------*(2*x*cos(2*x)*(x*x*x + 3) + sin(2*x)*(6 - x*x*x)) + sin(2*x)*(-4*(x*x*x + 3) - 3*x)|||
                                                                                                                       \  \                                                \                 (x*x*x + 3)    /                                                                                                                                                                                                                                          /                                                                                                                                                                     /                                                                                       \                         \                            \                 x*x*x + 3                                                                                    ///
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                      2                                                                                                                                                                                                                                                                                                                                                                                                                                               3                                                                                       
                                                                                                                                                                                                                                                                                                                                           (x*x*x + 3)                                                                                                                                                                                                                                                                                                                                                                                                                                     (x*x*x + 3)

$$\frac{\left(- 4 x^{2} - 2 x x\right) \left(x \left(x \left(\left(- 3 x - 4 \left(x x x + 3\right)\right) \sin{\left(2 x \right)} + \left(x x 6 \cos{\left(2 x \right)} - \frac{6 x}{x x x + 3} \left(2 x \cos{\left(2 x \right)} \left(x x x + 3\right) + \left(- x x x + 6\right) \sin{\left(2 x \right)}\right)\right)\right) + \left(x x x + 12\right) 2 \cos{\left(2 x \right)}\right) + \left(- x x x + 6\right) \sin{\left(2 x \right)}\right)}{\left(x x x + 3\right)^{3}} + \frac{- 3 x^{2} \sin{\left(2 x \right)} + x \left(\left(- 3 x - 4 \left(x x x + 3\right)\right) \sin{\left(2 x \right)} + \left(x x 6 \cos{\left(2 x \right)} - \frac{6 x}{x x x + 3} \left(2 x \cos{\left(2 x \right)} \left(x x x + 3\right) + \left(- x x x + 6\right) \sin{\left(2 x \right)}\right)\right)\right) + x \left(x x 6 \cos{\left(2 x \right)} + x \left(x \left(- 12 x \sin{\left(2 x \right)} + 6 \cos{\left(2 x \right)}\right) + x 6 \cos{\left(2 x \right)} - \frac{6 x \left(- 3 x^{2} \sin{\left(2 x \right)} + 2 x \left(2 x^{2} + x x\right) \cos{\left(2 x \right)} + 2 \left(- x x x + 6\right) \cos{\left(2 x \right)} + \left(x x x + 3\right) \left(- 4 x \sin{\left(2 x \right)} + 2 \cos{\left(2 x \right)}\right)\right)}{x x x + 3} + 2 \left(- 3 x - 4 \left(x x x + 3\right)\right) \cos{\left(2 x \right)} + \left(2 x \cos{\left(2 x \right)} \left(x x x + 3\right) + \left(- x x x + 6\right) \sin{\left(2 x \right)}\right) \left(- \frac{6 x \left(- 2 x^{2} - x x\right)}{\left(x x x + 3\right)^{2}} - \frac{6}{x x x + 3}\right) + \left(- 8 x^{2} - 4 x x - 3\right) \sin{\left(2 x \right)}\right) - \frac{6 x}{x x x + 3} \left(2 x \cos{\left(2 x \right)} \left(x x x + 3\right) + \left(- x x x + 6\right) \sin{\left(2 x \right)}\right) + \left(- 3 x - 4 \left(x x x + 3\right)\right) \sin{\left(2 x \right)} + 2 \left(2 x^{2} + x x\right) \cos{\left(2 x \right)} - 4 \left(x x x + 12\right) \sin{\left(2 x \right)}\right) + 2 \left(- x x x + 6\right) \cos{\left(2 x \right)} + \left(x x x + 12\right) 2 \cos{\left(2 x \right)}}{\left(x x x + 3\right)^{2}}$$

Simplificar

Segunda derivada [src]

  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         /                                                                                                        /    /                                                                                                                                                                                                                 /        3 \                                               \                                                                                                                          \                                                              \                                                                                                                                                                       \
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  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                        |    |                                                                                                                                                                                                               6*|1 - ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                                                                                                          |                                                              |                                                                                                                                                                       |
  |    /                                                                                                                                                                                                                 /         3 \                                               \     /    /                                                                                                                                                                                                                                                                                                                                  /         3 \                                                                                                                                                                                                                                                               /         3 \                                               \                                                                                                                                                                                                                                                            /         3 \                                               \                                                                                                                                                                       |  /                                                 /  /      3\                /     3\         \\     |    |                                                                                                            /     2              /      3\              /     3\                                 3         \     |         3|                                               |                                                                            /  /      3\                /     3\         \|                                                              |       /         3 \ /  /  /                                                 //     3\                /     3\         \\                       \                     \|
  |    |                                                                                                                                                                                                                 |      3*x  | /  /      3\                /     3\         \|     |    |                                                                                                                                                                                                                                                                                                                                  |      3*x  | /     3              /      3\              /     3\                                 2         \                                                                                                                                                            2 |      3*x  | /  /      3\                /     3\         \|                                                                                                                                                                                                                                                            |      3*x  | /  /      3\                /     3\         \|                                                                                                                                                                     2 |  |/              3\               2            6*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     |    |                  /              3\              /       2\                                             6*x*\- 3*x *sin(2*x) - 2*\-6 + x /*cos(2*x) - 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 6*x *cos(2*x)/     \    3 + x /                                               |   /              3\              /      3\                2            6*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     /      3\              /      3\               2         |       |      9*x  | |  |  |/              3\               2            6*x*\\6 - x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     /      3\         |   /      3\         ||
  |    |                                                                                                                                                                                                               6*|-1 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     |    |                                                                                                                                                                                                                                                                                                                                3*|-1 + ------|*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/                                                                                                                                                        18*x *|-2 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                                                                                                                                                                                                                                          6*|-1 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                                                                                                                                                  6*x *|x*|\12 + 3*x + 4*x /*sin(2*x) - 6*x *cos(2*x) + --------------------------------------------------| - x*|- x*|-6*x*cos(2*x) + 2*\12 + 3*x + 4*x /*cos(2*x) + 3*\1 + 4*x /*sin(2*x) + 6*x*(-cos(2*x) + 2*x*sin(2*x)) + ---------------------------------------------------------------------------------------------------- + -------------------------------------------------------------| - \12 + 3*x + 4*x /*sin(2*x) - 4*\12 + x /*sin(2*x) + 12*x *cos(2*x) - --------------------------------------------------| - 2*\12 + x /*cos(2*x) + 2*\-6 + x /*cos(2*x) + 3*x *sin(2*x)|   3*x*|-2 + ------|*|x*|x*|\12 + 3*x + 4*x /*sin(2*x) - 6*x *cos(2*x) + -----------------------------------------------| - 2*\12 + x /*cos(2*x)| + \-6 + x /*sin(2*x)||
  |    |                                                                                                            /     3              /      3\              /     3\                                 2         \     |          3|                                               |     |    |                                                                                                                     /     3              /      3\              /     3\                                 2         \      3 /     3              /      3\              /     3\                                 2         \     |          3|                                                                                                        /     2              /      3\                              2                                /     3\                              3         \         |          3|                                               |                                                                                                                                                       /     3              /      3\              /     3\                                 2         \     |          3|                                               |                                                                                                                 /  /      3\                /     3\         \        |  |                                                                        3                      |     |    |                                                                                                                                                            3                                                                                   3                           |                                                                                                   3                      |                                                              |       |          3| |  |  |                                                                       3                    |                       |                     ||
  |    |                  /              3\              /       2\                                             6*x*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     \     3 + x /                                               |     |    |                                                              /       2\              /              3\            3*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/   9*x *\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     \     3 + x /                                                                                                    6*x*\- 3*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 3*x *(-cos(2*x) + 2*x*sin(2*x)) + 4*\3 + x /*(x*cos(2*x) + sin(2*x)) + 6*x *sin(2*x)/         \     3 + x /                                               |                     /              3\              /       2\              /      3\                                                 2            6*x*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     \     3 + x /                                               |   /              3\              /      3\                             /      3\               2            6*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/        \  \                                                                   3 + x                       /     \    \                                                                                                                                                       3 + x                                                                               3 + x                            /                                                                                              3 + x                       /                                                              /       \     3 + x / \  \  \                                                                  3 + x                     /                       /                     /|
2*|- x*|-6*x*cos(2*x) + 2*\12 + 3*x + 4*x /*cos(2*x) + 3*\1 + 4*x /*sin(2*x) + 6*x*(-cos(2*x) + 2*x*sin(2*x)) - ---------------------------------------------------------------------------------------------------- - --------------------------------------------------------------| - x*|- x*|6*cos(2*x) - 24*x*sin(2*x) - 12*x*(x*cos(2*x) + sin(2*x)) - 6*\1 + 4*x /*cos(2*x) + 2*\12 + 3*x + 4*x /*sin(2*x) + -------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------| - 12*x*cos(2*x) + 2*\12 + 3*x + 4*x /*cos(2*x) + 3*\1 + 4*x /*sin(2*x) + 4*\12 + x /*cos(2*x) + 6*x*(-cos(2*x) + 2*x*sin(2*x)) + 12*x *sin(2*x) - ---------------------------------------------------------------------------------------------------- - --------------------------------------------------------------| - \12 + 3*x + 4*x /*sin(2*x) - 4*\12 + x /*sin(2*x) - 3*x*sin(2*x) + 2*\-6 + x /*sin(2*x) + 6*x *cos(2*x) - -------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  |    |                                                                                                                                                            3                                                                                   3                            |     |    |                                                                                                                                                                      3                                                                                                       2                                                                                                           3                                                                                                                                   3                                                                                                             2                             |                                                                                                                                                                                                       3                                                                                   3                            |                                                                                                                                        3                                                                                                                                                                                                                                                                                                                         3                                                                                                                                                                                                                                                                                                                                                                                 3                                                                               |
  |    \                                                                                                                                                       3 + x                                                                               3 + x                             /     |    |                                                                                                                                                                 3 + x                                                                                                /     3\                                                                                                       3 + x                                                                                                                               3 + x                                                                                                      /     3\                              |                                                                                                                                                                                                  3 + x                                                                               3 + x                             |                                                                                                                                   3 + x                                                                                                                                                                                                                                                                                                                     3 + x                                                                                                                                                                                                                                                                                                                                                                             3 + x                                                                                |
  \                                                                                                                                                                                                                                                                                        \    \                                                                                                                                                                                                                                                                      \3 + x /                                                                                                                                                                                                                                                                                                                                                      \3 + x /                              /                                                                                                                                                                                                                                                                                                                        /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /     3\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \3 + x /

$$\frac{2 \left(6 x^{2} \cos{\left(2 x \right)} + \frac{6 x^{2} \left(3 x^{2} \sin{\left(2 x \right)} + x \left(- 6 x^{2} \cos{\left(2 x \right)} + \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} + \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right) - x \left(12 x^{2} \cos{\left(2 x \right)} - x \left(6 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 6 x \cos{\left(2 x \right)} + \frac{6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} - 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 3 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} + \frac{6 \left(- \frac{3 x^{3}}{x^{3} + 3} + 1\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3}\right) - \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} - 4 \left(x^{3} + 12\right) \sin{\left(2 x \right)} - \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} - 2 \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right)}{x^{3} + 3} - x \left(6 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 6 x \cos{\left(2 x \right)} - \frac{6 x \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 3 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} - \frac{6 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3}\right) - x \left(12 x^{2} \sin{\left(2 x \right)} + 6 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - x \left(- \frac{9 x^{3} \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{2}} - \frac{18 x^{2} \left(\frac{3 x^{3}}{x^{3} + 3} - 2\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{\left(x^{3} + 3\right)^{2}} - 12 x \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) - 24 x \sin{\left(2 x \right)} + \frac{6 x \left(6 x^{3} \sin{\left(2 x \right)} + 3 x^{2} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x^{2} \cos{\left(2 x \right)} + 3 x \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 3\right) \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)\right)}{x^{3} + 3} - 6 \left(4 x^{2} + 1\right) \cos{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)} + 6 \cos{\left(2 x \right)} - \frac{3 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} + \frac{3 \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3}\right) - 12 x \cos{\left(2 x \right)} - \frac{6 x \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 3 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 12\right) \cos{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} - \frac{6 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3}\right) - 3 x \sin{\left(2 x \right)} - \frac{3 x \left(x \left(x \left(- 6 x^{2} \cos{\left(2 x \right)} + \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} + \left(6 - x^{3}\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} + \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right) - 2 \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right) + \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right) \left(\frac{9 x^{3}}{x^{3} + 3} - 2\right)}{x^{3} + 3} - \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} + 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} - 4 \left(x^{3} + 12\right) \sin{\left(2 x \right)} - \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right)}{\left(x^{3} + 3\right)^{2}}$$

Simplificar

Tercera derivada [src]

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             /  /                                                                                                                                                                                                                 /         3 \                                               \     /  /                                                                                                                                                                                                                                                                                                                                                                                /         3 \                                                                                                                                                                                                                  /         3 \                                               \                                                       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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |  |                                                                                                                                                                                                                 |      3*x  | /  /      3\                /     3\         \|     |  |                                                                                                                                                                                                                                                                                                                                                                                |      3*x  | /     3              /      3\              /     3\                                 2         \                                                                                                               2 |      3*x  | /  /      3\                /     3\         \|                                                                                                                                                                                                                                                            |      3*x  | /  /      3\                /     3\         \|                                                                                                                                                               |                                                                                       /                                                                                                        /  /                                                                                                                                                                                                                 /        3 \                                               \                                                                                                                          \                                                              \|
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |  |                                                                                                                                                                                                               6*|-1 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     |  |                                                                                                                                                                                                                                                                                                                                                                              3*|-1 + ------|*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/                                                                                                           18*x *|-2 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                                                                                                                                                                                                                                          6*|-1 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                                                                                                                                               |                                                                                       |                                                                                                        |  |                                                                                                                                                                                                                 |     3*x  | /  /      3\                /     3\         \|                                                                                                                          |                                                              ||
  |                /                                                                                                                                                                              /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /        3          6  \                                                                                                                       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /  /  /                                                 /  /      3\                /     3\         \\                       \                     \ /        3          6  \                                                                                                                 |  |                                                                                                            /     3              /      3\              /     3\                                 2         \     |          3|                                               |     |  |                /     3              /      3\              /     3\                                 2         \                                                                                                             /     2              /      3\                              2                                /     3\                              3         \     |          3|                                                                                                       3 /     3              /      3\              /     3\                                 2         \         |          3|                                               |                                                                                                                                                       /     3              /      3\              /     3\                                 2         \     |          3|                                               |                                                                                                                 /  /      3\                /     3\         \|                                                                                       |                                                                                                        |  |                                                                                                                                                                                                               6*|1 - ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                                                                                                          |                                                              ||
  |                |                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /         3 \                                                                                                                                                                                                                                                                                                                                                                                                                                                      /  /      3\                /     3\         \ |    27*x       27*x   |         /         3 \                                                                                                 |                                                                                                                                                                                                                                                     /         3 \                                                                                                                                                                                                                   /         3 \                                               |                                                                                                                                         /                                                                                                                                                                                                                                                                                                                                                                                /         3 \                                                                                                                                                                                                                  /         3 \                                               \                                            |  |  |/              3\               2            6*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     /      3\         |   /      3\         | |    27*x       54*x   |                                                                                                               2 |  |                  /              3\              /       2\                                             6*x*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     \     3 + x /                                               |     |  |              3*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     /              3\              /       2\                                                           6*x*\- 3*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 3*x *(-cos(2*x) + 2*x*sin(2*x)) + 4*\3 + x /*(x*cos(2*x) + sin(2*x)) + 6*x *sin(2*x)/     \     3 + x /                                                                                                    9*x *\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/         \     3 + x /                                               |                     /              3\              /       2\              /      3\                                                 2            6*x*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     \     3 + x /                                               |   /              3\               2              /      3\                             /      3\            6*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|      /         3 \                                                      /         3 \ |  /                                                 /  /      3\                /     3\         \\     |  |                                                                                                            /     2              /      3\              /     3\                                 3         \     |         3|                                               |                                                                            /  /      3\                /     3\         \|                                                              ||
  |                |                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |      3*x  | /     2              /      3\                              2                                /     3\                              3         \                                                                                                                                                                                                                                                                                                   9*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/*|4 - ------ + ---------|       2 |      3*x  | /     3              /      3\              /     3\                                 2         \|                                                                                                                                                                                                                                                     |      3*x  | /     3              /      3\              /     3\                                 2         \                                                                                                                2 |      3*x  | /  /      3\                /     3\         \|                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                |      3*x  | /     3              /      3\              /     3\                                 2         \                                                                                                               2 |      3*x  | /  /      3\                /     3\         \|                                          6*|x*|x*|\12 + 3*x + 4*x /*sin(2*x) - 6*x *cos(2*x) + --------------------------------------------------| - 2*\12 + x /*cos(2*x)| + \-6 + x /*sin(2*x)|*|1 - ------ + ---------|                                                                                                           18*x *|x*|-6*x*cos(2*x) + 2*\12 + 3*x + 4*x /*cos(2*x) + 3*\1 + 4*x /*sin(2*x) + 6*x*(-cos(2*x) + 2*x*sin(2*x)) - ---------------------------------------------------------------------------------------------------- - --------------------------------------------------------------| + x*|x*|-6*cos(2*x) - -------------------------------------------------------------------------------------------------- - 2*\12 + 3*x + 4*x /*sin(2*x) + 6*\1 + 4*x /*cos(2*x) + 12*x*(x*cos(2*x) + sin(2*x)) + 24*x*sin(2*x) - -------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------| - 12*x*cos(2*x) + 2*\12 + 3*x + 4*x /*cos(2*x) + 3*\1 + 4*x /*sin(2*x) + 4*\12 + x /*cos(2*x) + 6*x*(-cos(2*x) + 2*x*sin(2*x)) + 12*x *sin(2*x) - ---------------------------------------------------------------------------------------------------- - --------------------------------------------------------------| + \12 + 3*x + 4*x /*sin(2*x) - 6*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 4*\12 + x /*sin(2*x) + --------------------------------------------------|      |      3*x  | /  /      3\                /     3\         \       |      9*x  | |  |/              3\               2            6*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     |  |                  /              3\              /       2\                                             6*x*\- 3*x *sin(2*x) - 2*\-6 + x /*cos(2*x) - 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 6*x *cos(2*x)/     \    3 + x /                                               |   /              3\                2              /      3\            6*x*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|     /      3\              /      3\               2         ||
  |                |                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            3*|-1 + ------|*\- 3*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 3*x *(-cos(2*x) + 2*x*sin(2*x)) + 4*\3 + x /*(x*cos(2*x) + sin(2*x)) + 6*x *sin(2*x)/                                                                                                                                                                                                                                                                                                                                                      |         3           2|   18*x *|-2 + ------|*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/|                                                                                                                                                                                                                                                   9*|-1 + ------|*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/                                                                                                            54*x *|-2 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                              3*|-1 + ------|*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/                                                                                                           18*x *|-2 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/|                                            |  |  |                                                                        3                      |                       |                     | |         3           2|                                                                                                                 |  |                                                                                                                                                            3                                                                                   3                            |     |  |                                                                 3                                                                                                                                                                                                                                  3                                                                                                                                   3                                                                                                              2                                                                                     2                             |                                                                                                                                                                                                       3                                                                                   3                            |                                                                                                                                        3                      |   18*|-1 + ------|*\- \-6 + x /*sin(2*x) + 2*x*\3 + x /*cos(2*x)/   9*x*|-2 + ------|*|x*|\12 + 3*x + 4*x /*sin(2*x) - 6*x *cos(2*x) + --------------------------------------------------| + x*|x*|-6*x*cos(2*x) + 2*\12 + 3*x + 4*x /*cos(2*x) + 3*\1 + 4*x /*sin(2*x) + 6*x*(-cos(2*x) + 2*x*sin(2*x)) + ---------------------------------------------------------------------------------------------------- + -------------------------------------------------------------| + \12 + 3*x + 4*x /*sin(2*x) - 12*x *cos(2*x) + 4*\12 + x /*sin(2*x) + --------------------------------------------------| - 2*\12 + x /*cos(2*x) + 2*\-6 + x /*cos(2*x) + 3*x *sin(2*x)||
  |                |                 /     3              /      3\              /     3\                                 2         \                                                             |                                                                                                   /     2              /      3\                              2                                /     3\                              3         \                               2 /     3              /      3\              /     3\                                 2         \       3 /     2              /      3\                              2                                /     3\                              3         \     |          3|                                                                                                                                                      /               /      3\              /     3\                                                                     3                2                2                        \       5 /     3              /      3\              /     3\                                 2         \                                                      |    3 + x    /     3\ |         |          3|                                                                                                 |                                                                                                  /     2              /      3\                              2                                /     3\                              3         \     |          3|                                                                                                        3 /     3              /      3\              /     3\                                 2         \         |          3|                                               |                                                                                                                                         |                /     3              /      3\              /     3\                                 2         \                                                                                                             /     2              /      3\                              2                                /     3\                              3         \     |          3|                                                                                                       3 /     3              /      3\              /     3\                                 2         \         |          3|                                               |                                            \  \  \                                                                   3 + x                       /                       /                     / |    3 + x    /     3\ |        /     3              /      3\              /     3\                                 2         \         |  \                                                                                                                                                       3 + x                                                                               3 + x                             /     |  |                                                            3 + x                                                                                                                                                                                                                              3 + x                                                                                                                               3 + x                                                                                                       /     3\                                                                              /     3\                              |                                                                                                                                                                                                  3 + x                                                                               3 + x                             |                                                                                                                                   3 + x                       |      |          3|                                                      |          3| |  |                                                                        3                      |     |  |                                                                                                                                                            3                                                                                   3                           |                                                                                                   3                      |                                                              ||
  |                |               9*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     /      3\              /              3\                |                                 /              3\                                               6*\- 3*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 3*x *(-cos(2*x) + 2*x*sin(2*x)) + 4*\3 + x /*(x*cos(2*x) + sin(2*x)) + 6*x *sin(2*x)/     /       2\            18*x *\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/   18*x *\- 3*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 3*x *(-cos(2*x) + 2*x*sin(2*x)) + 4*\3 + x /*(x*cos(2*x) + sin(2*x)) + 6*x *sin(2*x)/     \     3 + x /                                                                                                                                                  3*x*\3*sin(2*x) - 4*\-6 + x /*cos(2*x) - 4*\3 + x /*(-3*cos(2*x) + 2*x*sin(2*x)) + 6*x*(-cos(2*x) + 2*x*sin(2*x)) + 12*x *cos(2*x) + 18*x *sin(2*x) + 24*x *(x*cos(2*x) + sin(2*x))/   27*x *\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/                                                      \             \3 + x / /         \     3 + x /                                                                                                 |      /       2\                                               2                             18*x*\- 3*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 3*x *(-cos(2*x) + 2*x*sin(2*x)) + 4*\3 + x /*(x*cos(2*x) + sin(2*x)) + 6*x *sin(2*x)/     \     3 + x /                                                                                                    27*x *\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/         \     3 + x /                                               |                                         2               /      3\              /       2\              /              3\                |              3*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/     /              3\              /       2\                                                           6*x*\- 3*x *cos(2*x) - 2*\-6 + x /*sin(2*x) + 3*x*sin(2*x) + 3*x *(-cos(2*x) + 2*x*sin(2*x)) + 4*\3 + x /*(x*cos(2*x) + sin(2*x)) + 6*x *sin(2*x)/     \     3 + x /                                                                                                    9*x *\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/         \     3 + x /                                               |     /      3\                                                                                                                                                                                    \             \3 + x / /   18*x*\- 6*x *cos(2*x) + 2*\-6 + x /*cos(2*x) + 2*\3 + x /*(-cos(2*x) + 2*x*sin(2*x)) + 3*x *sin(2*x)/         \                                                                                                                                                                                                                                                                                      \  \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \3 + x /                                                                              \3 + x /                              /                                                                                                                                                                                                                                                                                                                        /                                                                                                                                                               /      \     3 + x /                                                      \     3 + x / \  \                                                                   3 + x                       /     \  \                                                                                                                                                       3 + x                                                                               3 + x                            /                                                                                              3 + x                       /                                                              /|
2*|-3*sin(2*x) - x*|-24*cos(2*x) - -------------------------------------------------------------------------------------------------- - 8*\12 + x /*sin(2*x) - 6*\12 + 3*x + 4*x /*sin(2*x) - 2*x*|-24*sin(2*x) - 54*x*cos(2*x) + 2*\12 + 3*x + 4*x /*cos(2*x) + 6*x*(-3*cos(2*x) + 2*x*sin(2*x)) + ------------------------------------------------------------------------------------------------------------------------------------------------ + 9*\1 + 4*x /*sin(2*x) - ------------------------------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------| + 18*\1 + 4*x /*cos(2*x) + 36*x*(x*cos(2*x) + sin(2*x)) + 36*x *cos(2*x) + 108*x*sin(2*x) - --------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------| - 18*x*(-cos(2*x) + 2*x*sin(2*x)) - 18*x *sin(2*x) - 12*\12 + x /*cos(2*x) - 9*\1 + 4*x /*sin(2*x) - 6*\12 + 3*x + 4*x /*cos(2*x) - 3*x*|-6*cos(2*x) - -------------------------------------------------------------------------------------------------- - 2*\12 + 3*x + 4*x /*sin(2*x) + 6*\1 + 4*x /*cos(2*x) + 12*x*(x*cos(2*x) + sin(2*x)) + 24*x*sin(2*x) - -------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------| + 4*\-6 + x /*cos(2*x) + 18*x*cos(2*x) + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  |                |                                                                  3                                                                                                           |                                                                                                                                                                           3                                                                                                                                                      2                                                                                                                               2                                                                                                                                                          3                                                                                                                                                                           3                                                                                                                                                3                                                                                           2                                                                                                 2                                                      |                                                                                                                                                                         3                                                                                                                                   3                                                                                                              2                                                                                      2                             |                                                                                                                                         |                                                                 3                                                                                                                                                                                                                                  3                                                                                                                                   3                                                                                                              2                                                                                     2                             |                                                                                                                                    3                                                                                                                                             3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       3                                                                                                                                                                                                                                                                                              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  |                |                                                             3 + x                                                                                                            |                                                                                                                                                                      3 + x                                                                                                                                               /     3\                                                                                                                        /     3\                                                                                                                                                      3 + x                                                                                                                                                                       3 + x                                                                                                                                         /     3\                                                                                    /     3\                                                                                          /     3\                                                       |                                                                                                                                                                    3 + x                                                                                                                               3 + x                                                                                                       /     3\                                                                               /     3\                              |                                                                                                                                         |                                                            3 + x                                                                                                                                                                                                                              3 + x                                                                                                                               3 + x                                                                                                       /     3\                                                                              /     3\                              |                                                                                                                               3 + x                                                                                                                                         3 + x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   3 + x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 3 + x                                                                                                                                                                                                                                                                                                                                3 + x                                                                                                                                                                                                                             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                                                                                                            \3 + x /                                                                                    \3 + x /                                                                                          \3 + x /                                                       /                                                                                                                                                                                                                                                                                                                                                                                                                    \3 + x /                                                                               \3 + x /                              /                                                                                                             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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /     3\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \3 + x /

$$\frac{2 \left(- 18 x^{2} \sin{\left(2 x \right)} + \frac{18 x^{2} \left(- 6 x^{2} \cos{\left(2 x \right)} + x \left(6 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 6 x \cos{\left(2 x \right)} - \frac{6 x \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 3 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} - \frac{6 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3}\right) + x \left(12 x^{2} \sin{\left(2 x \right)} + 6 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) + x \left(\frac{9 x^{3} \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{2}} + \frac{18 x^{2} \left(\frac{3 x^{3}}{x^{3} + 3} - 2\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{\left(x^{3} + 3\right)^{2}} + 12 x \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) + 24 x \sin{\left(2 x \right)} - \frac{6 x \left(6 x^{3} \sin{\left(2 x \right)} + 3 x^{2} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x^{2} \cos{\left(2 x \right)} + 3 x \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 3\right) \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 6 \left(4 x^{2} + 1\right) \cos{\left(2 x \right)} - 2 \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)} - 6 \cos{\left(2 x \right)} + \frac{3 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} - \frac{3 \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3}\right) - 12 x \cos{\left(2 x \right)} - \frac{6 x \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 3 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 12\right) \cos{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} - \frac{6 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3}\right) + 3 x \sin{\left(2 x \right)} + \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 12\right) \sin{\left(2 x \right)} + \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} - 18 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x \left(\frac{9 x^{3} \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{2}} + \frac{18 x^{2} \left(\frac{3 x^{3}}{x^{3} + 3} - 2\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{\left(x^{3} + 3\right)^{2}} + 12 x \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) + 24 x \sin{\left(2 x \right)} - \frac{6 x \left(6 x^{3} \sin{\left(2 x \right)} + 3 x^{2} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x^{2} \cos{\left(2 x \right)} + 3 x \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 3\right) \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 6 \left(4 x^{2} + 1\right) \cos{\left(2 x \right)} - 2 \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)} - 6 \cos{\left(2 x \right)} + \frac{3 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} - \frac{3 \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3}\right) - x \left(\frac{27 x^{3} \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{2}} + 36 x^{2} \cos{\left(2 x \right)} + \frac{54 x^{2} \left(\frac{3 x^{3}}{x^{3} + 3} - 2\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{\left(x^{3} + 3\right)^{2}} + 36 x \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) - 2 x \left(\frac{27 x^{5} \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{3}} - \frac{18 x^{3} \left(6 x^{3} \sin{\left(2 x \right)} + 3 x^{2} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x^{2} \cos{\left(2 x \right)} + 3 x \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 3\right) \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{2}} + \frac{18 x^{2} \left(\frac{3 x^{3}}{x^{3} + 3} - 2\right) \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{2}} - \frac{18 x^{2} \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{\left(x^{3} + 3\right)^{2}} + 6 x \left(2 x \sin{\left(2 x \right)} - 3 \cos{\left(2 x \right)}\right) - 54 x \cos{\left(2 x \right)} + \frac{3 x \left(12 x^{3} \cos{\left(2 x \right)} + 24 x^{2} \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) + 18 x^{2} \sin{\left(2 x \right)} + 6 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 4 \left(x^{3} - 6\right) \cos{\left(2 x \right)} - 4 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - 3 \cos{\left(2 x \right)}\right) + 3 \sin{\left(2 x \right)}\right)}{x^{3} + 3} + \frac{9 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right) \left(\frac{27 x^{6}}{\left(x^{3} + 3\right)^{2}} - \frac{27 x^{3}}{x^{3} + 3} + 4\right)}{\left(x^{3} + 3\right)^{2}} + 9 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} - 24 \sin{\left(2 x \right)} - \frac{3 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(6 x^{3} \sin{\left(2 x \right)} + 3 x^{2} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x^{2} \cos{\left(2 x \right)} + 3 x \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 3\right) \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)\right)}{x^{3} + 3} + \frac{6 \left(6 x^{3} \sin{\left(2 x \right)} + 3 x^{2} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x^{2} \cos{\left(2 x \right)} + 3 x \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 3\right) \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)\right)}{x^{3} + 3}\right) + 108 x \sin{\left(2 x \right)} - \frac{18 x \left(6 x^{3} \sin{\left(2 x \right)} + 3 x^{2} \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 3 x^{2} \cos{\left(2 x \right)} + 3 x \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \sin{\left(2 x \right)} + 4 \left(x^{3} + 3\right) \left(x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 18 \left(4 x^{2} + 1\right) \cos{\left(2 x \right)} - 8 \left(x^{3} + 12\right) \sin{\left(2 x \right)} - 6 \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)} - 24 \cos{\left(2 x \right)} + \frac{9 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} - \frac{9 \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3}\right) + 18 x \cos{\left(2 x \right)} - \frac{9 x \left(\frac{9 x^{3}}{x^{3} + 3} - 2\right) \left(3 x^{2} \sin{\left(2 x \right)} + x \left(- 6 x^{2} \cos{\left(2 x \right)} + \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} + \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right) + x \left(- 12 x^{2} \cos{\left(2 x \right)} + x \left(6 x \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) - 6 x \cos{\left(2 x \right)} + \frac{6 x \left(6 x^{3} \cos{\left(2 x \right)} - 3 x^{2} \sin{\left(2 x \right)} - 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} - 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} + 3 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 2 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} + \frac{6 \left(- \frac{3 x^{3}}{x^{3} + 3} + 1\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3}\right) + \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} + 4 \left(x^{3} + 12\right) \sin{\left(2 x \right)} + \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right) + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} - 2 \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right)}{x^{3} + 3} + \frac{18 x \left(- 6 x^{3} \cos{\left(2 x \right)} + 3 x^{2} \sin{\left(2 x \right)} + 2 \left(x^{3} - 6\right) \cos{\left(2 x \right)} + 2 \left(x^{3} + 3\right) \left(2 x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right)\right)}{x^{3} + 3} - 9 \left(4 x^{2} + 1\right) \sin{\left(2 x \right)} + 4 \left(x^{3} - 6\right) \cos{\left(2 x \right)} - 12 \left(x^{3} + 12\right) \cos{\left(2 x \right)} - 6 \left(4 x^{3} + 3 x + 12\right) \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} + \frac{6 \left(x \left(x \left(- 6 x^{2} \cos{\left(2 x \right)} + \frac{6 x \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3} + \left(4 x^{3} + 3 x + 12\right) \sin{\left(2 x \right)}\right) - 2 \left(x^{3} + 12\right) \cos{\left(2 x \right)}\right) + \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right) \left(\frac{54 x^{6}}{\left(x^{3} + 3\right)^{2}} - \frac{27 x^{3}}{x^{3} + 3} + 1\right)}{x^{3} + 3} + \frac{18 \left(\frac{3 x^{3}}{x^{3} + 3} - 1\right) \left(2 x \left(x^{3} + 3\right) \cos{\left(2 x \right)} - \left(x^{3} - 6\right) \sin{\left(2 x \right)}\right)}{x^{3} + 3}\right)}{\left(x^{3} + 3\right)^{2}}$$

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Gráfico

Derivada de (x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))

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Derivada de (xxx+3)^(-2)(sin(2x)(6-xxx)+x(2cos(2x)(xxx+12)+x(6cos(2x)xx-6x/(xxx+3)(2xcos(2x)(xxx+3)+sin(2x)(6-xxx))+sin(2x)(-4(xxx+3)-3x))))

Gráfico:

Definida a trozos:

Solución

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Derivada de (x*x*x+3)^(-2)*(sin(2*x)*(6-x*x*x)+x*(2*cos(2*x)*(x*x*x+12)+x*(6*cos(2*x)*x*x-6*x/(x*x*x+3)*(2*x*cos(2*x)*(x*x*x+3)+sin(2*x)*(6-x*x*x))+sin(2*x)*(-4*(x*x*x+3)-3*x))))

Gráfico:

Definida a trozos:

Solución

Derivada de (xxx+3)^(-2)(sin(2x)(6-xxx)+x(2cos(2x)(xxx+12)+x(6cos(2x)xx-6x/(xxx+3)(2xcos(2x)(xxx+3)+sin(2x)(6-xxx))+sin(2x)(-4(xxx+3)-3x))))