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Derivada de (π-2x)³
Derivada de y=e×
Derivada de y/(sqrt(5^2+y^2))
Derivada de y=(3x-7)4
Expresiones idénticas
x*exp(-(-33cos(t)*80sin(dos t)+33sin(t)*40cos(dos t))/(1089cos^2(t)+1600cos^2(2t))x)
x multiplicar por exponente de ( menos ( menos 33 coseno de (t) multiplicar por 80 seno de (2t) más 33 seno de (t) multiplicar por 40 coseno de (2t)) dividir por (1089 coseno de al cuadrado (t) más 1600 coseno de al cuadrado (2t))x)
x multiplicar por exponente de ( menos ( menos 33 coseno de (t) multiplicar por 80 seno de (dos t) más 33 seno de (t) multiplicar por 40 coseno de (dos t)) dividir por (1089 coseno de al cuadrado (t) más 1600 coseno de al cuadrado (2t))x)
x*exp(-(-33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos2(t)+1600cos2(2t))x)
x*exp--33cost*80sin2t+33sint*40cos2t/1089cos2t+1600cos22tx
x*exp(-(-33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos²(t)+1600cos²(2t))x)
x*exp(-(-33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos en el grado 2(t)+1600cos en el grado 2(2t))x)
xexp(-(-33cos(t)80sin(2t)+33sin(t)40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)
xexp(-(-33cos(t)80sin(2t)+33sin(t)40cos(2t))/(1089cos2(t)+1600cos2(2t))x)
xexp--33cost80sin2t+33sint40cos2t/1089cos2t+1600cos22tx
xexp--33cost80sin2t+33sint40cos2t/1089cos^2t+1600cos^22tx
x*exp(-(-33cos(t)*80sin(2t)+33sin(t)*40cos(2t)) dividir por (1089cos^2(t)+1600cos^2(2t))x)
Expresiones semejantes
x*exp(-(-33cos(t)*80sin(2t)-33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)
x*exp(-(-33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)-1600cos^2(2t))x)
x*exp((-33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)
x*exp(-(33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)

Derivada de la función/ x*exp(-(-33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)

Derivada de xexp(-(-33cos(t)80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)

Solución

Ha introducido [src]

   --33*cos(t)*80*sin(2*t) - 33*sin(t)*40*cos(2*t)  
   -----------------------------------------------*x
                    2              2                
            1089*cos (t) + 1600*cos (2*t)           
x*e

$$x e^{x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}$$

x*exp(((-(-33*cos(t))*80*sin(2*t) - (33*sin(t))*40*cos(2*t))/(1089*cos(t)^2 + 1600*cos(2*t)^2))*x)

Solución detallada

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 $1$
$g{\left(x \right)} = e^{x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. Sustituimos $u = x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}$ .
2. Derivado $e^{u}$ es.
3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{\partial}{\partial x} x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}$ :
  1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
    1. Según el principio, aplicamos: $x$ tenemos $1$
    Entonces, como resultado: $\frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}$
  Como resultado de la secuencia de reglas:
  
  $\frac{\left(- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}\right) e^{x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}$
Como resultado de: $\frac{x \left(- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}\right) e^{x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}} + e^{x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}$
Simplificamos:

$\frac{\left(- 2640 x \sin^{3}{\left(t \right)} + 3960 x \sin{\left(t \right)} + 6400 \sin^{4}{\left(t \right)} - 7489 \sin^{2}{\left(t \right)} + 2689\right) e^{- \frac{1320 x \left(2 \sin^{2}{\left(t \right)} - 3\right) \sin{\left(t \right)}}{6400 \sin^{4}{\left(t \right)} - 7489 \sin^{2}{\left(t \right)} + 2689}}}{6400 \sin^{4}{\left(t \right)} - 7489 \sin^{2}{\left(t \right)} + 2689}$

Respuesta:

$\frac{\left(- 2640 x \sin^{3}{\left(t \right)} + 3960 x \sin{\left(t \right)} + 6400 \sin^{4}{\left(t \right)} - 7489 \sin^{2}{\left(t \right)} + 2689\right) e^{- \frac{1320 x \left(2 \sin^{2}{\left(t \right)} - 3\right) \sin{\left(t \right)}}{6400 \sin^{4}{\left(t \right)} - 7489 \sin^{2}{\left(t \right)} + 2689}}}{6400 \sin^{4}{\left(t \right)} - 7489 \sin^{2}{\left(t \right)} + 2689}$

Primera derivada [src]

                                                     --33*cos(t)*80*sin(2*t) - 33*sin(t)*40*cos(2*t)                                                       
                                                     -----------------------------------------------*x    --33*cos(t)*80*sin(2*t) - 33*sin(t)*40*cos(2*t)  
                                                                      2              2                    -----------------------------------------------*x
                                                              1089*cos (t) + 1600*cos (2*t)                                2              2                
x*(--33*cos(t)*80*sin(2*t) - 33*sin(t)*40*cos(2*t))*e                                                              1089*cos (t) + 1600*cos (2*t)           
------------------------------------------------------------------------------------------------------ + e                                                 
                                            2              2                                                                                               
                                    1089*cos (t) + 1600*cos (2*t)

$$\frac{x \left(- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}\right) e^{x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}} + e^{x \frac{- 40 \cdot 33 \sin{\left(t \right)} \cos{\left(2 t \right)} - 80 \left(- 33 \cos{\left(t \right)}\right) \sin{\left(2 t \right)}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}$$

Simplificar

Segunda derivada [src]

                                                                                               -1320*x*(cos(2*t)*sin(t) - 2*cos(t)*sin(2*t))
                                                                                               ---------------------------------------------
                                                                                                               2              2             
     /     660*x*(cos(2*t)*sin(t) - 2*cos(t)*sin(2*t))\                                                1089*cos (t) + 1600*cos (2*t)        
2640*|-1 + -------------------------------------------|*(cos(2*t)*sin(t) - 2*cos(t)*sin(2*t))*e                                             
     |                    2              2            |                                                                                     
     \            1089*cos (t) + 1600*cos (2*t)       /                                                                                     
--------------------------------------------------------------------------------------------------------------------------------------------
                                                               2              2                                                             
                                                       1089*cos (t) + 1600*cos (2*t)

$$\frac{2640 \left(\sin{\left(t \right)} \cos{\left(2 t \right)} - 2 \sin{\left(2 t \right)} \cos{\left(t \right)}\right) \left(\frac{660 x \left(\sin{\left(t \right)} \cos{\left(2 t \right)} - 2 \sin{\left(2 t \right)} \cos{\left(t \right)}\right)}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}} - 1\right) e^{- \frac{1320 x \left(\sin{\left(t \right)} \cos{\left(2 t \right)} - 2 \sin{\left(2 t \right)} \cos{\left(t \right)}\right)}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}$$

Simplificar

Tercera derivada [src]

                                                                                                  -1320*x*(cos(2*t)*sin(t) - 2*cos(t)*sin(2*t))
                                                                                                  ---------------------------------------------
                                                                                                                  2              2             
                                             2 /    440*x*(cos(2*t)*sin(t) - 2*cos(t)*sin(2*t))\          1089*cos (t) + 1600*cos (2*t)        
5227200*(cos(2*t)*sin(t) - 2*cos(t)*sin(2*t)) *|1 - -------------------------------------------|*e                                             
                                               |                   2              2            |                                               
                                               \           1089*cos (t) + 1600*cos (2*t)       /                                               
-----------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       2                                                       
                                                        /        2              2     \                                                        
                                                        \1089*cos (t) + 1600*cos (2*t)/

$$\frac{5227200 \left(\sin{\left(t \right)} \cos{\left(2 t \right)} - 2 \sin{\left(2 t \right)} \cos{\left(t \right)}\right)^{2} \left(- \frac{440 x \left(\sin{\left(t \right)} \cos{\left(2 t \right)} - 2 \sin{\left(2 t \right)} \cos{\left(t \right)}\right)}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}} + 1\right) e^{- \frac{1320 x \left(\sin{\left(t \right)} \cos{\left(2 t \right)} - 2 \sin{\left(2 t \right)} \cos{\left(t \right)}\right)}{1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}}}}{\left(1089 \cos^{2}{\left(t \right)} + 1600 \cos^{2}{\left(2 t \right)}\right)^{2}}$$

Simplificar

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Expresiones idénticas

Expresiones semejantes

Derivada de xexp(-(-33cos(t)80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)

Gráfico:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de x*exp(-(-33cos(t)*80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)

Gráfico:

Definida a trozos:

Solución

Derivada de xexp(-(-33cos(t)80sin(2t)+33sin(t)*40cos(2t))/(1089cos^2(t)+1600cos^2(2t))x)