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Derivada de la función/ ((x*(x^3+1)*sin2x)/(x-2))^(1/3)

Derivada de ((x(x^3+1)sin2x)/(x-2))^(1/3)

Solución

Ha introducido [src]

     _____________________
    /   / 3    \          
   /  x*\x  + 1/*sin(2*x) 
3 /   ------------------- 
\/           x - 2

$$\sqrt[3]{\frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}}$$

(((x*(x^3 + 1))*sin(2*x))/(x - 2))^(1/3)

Solución detallada

Sustituimos $u = \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}$ .
Según el principio, aplicamos: $\sqrt[3]{u}$ tenemos $\frac{1}{3 u^{\frac{2}{3}}}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}$ :
1. Se aplica la regla de la derivada parcial:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x \left(x^{3} + 1\right) \sin{\left(2 x \right)}$ y $g{\left(x \right)} = x - 2$ .
  
  Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
  1. 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 $\frac{d}{d x} f{\left(x \right)}$ :
    1. Según el principio, aplicamos: $x$ tenemos $1$
    $g{\left(x \right)} = x^{3} + 1$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. diferenciamos $x^{3} + 1$ miembro por miembro:
      1. La derivada de una constante $1$ es igual a cero.
      2. Según el principio, aplicamos: $x^{3}$ tenemos $3 x^{2}$
      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: $3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}$
  Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
  1. diferenciamos $x - 2$ miembro por miembro:
    1. La derivada de una constante $-2$ es igual a cero.
    2. Según el principio, aplicamos: $x$ tenemos $1$
    Como resultado de: $1$
  Ahora aplicamos la regla de la derivada de una divesión:
  
  $\frac{- x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \left(x - 2\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{\left(x - 2\right)^{2}}$
Como resultado de la secuencia de reglas:

$\frac{- x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \left(x - 2\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 \left(\frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)^{\frac{2}{3}} \left(x - 2\right)^{2}}$
Simplificamos:

$\frac{- x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \left(x - 2\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 \left(\frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)^{\frac{2}{3}} \left(x - 2\right)^{2}}$

Respuesta:

$\frac{- x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \left(x - 2\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 \left(\frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)^{\frac{2}{3}} \left(x - 2\right)^{2}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

     _____________________                                                                            
    /   / 3    \                   //       3\                / 3    \              / 3    \         \
   /  x*\x  + 1/*sin(2*x)          |\1 + 4*x /*sin(2*x) + 2*x*\x  + 1/*cos(2*x)   x*\x  + 1/*sin(2*x)|
3 /   ------------------- *(x - 2)*|------------------------------------------- - -------------------|
\/           x - 2                 |                 3*(x - 2)                                  2    |
                                   \                                                   3*(x - 2)     /
------------------------------------------------------------------------------------------------------
                                           / 3    \                                                   
                                         x*\x  + 1/*sin(2*x)

$$\frac{\sqrt[3]{\frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}} \left(x - 2\right) \left(- \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{3 \left(x - 2\right)^{2}} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}}{3 \left(x - 2\right)}\right)}{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}$$

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

                           /                                                                              /  /       3\                /     3\                                               //     3\            /       3\               3               2                /     3\         \                                                                     3              /     3\              /     3\                                       2               3                /     3\                /     3\                /     3\         \                                                                               //       3\                /     3\                                                                                           /     3\               3                                        /     3\                /     3\         \                                                                                    //       3\                /     3\                                                                                           /     3\               3                                        /     3\                /     3\         \     //       3\                /     3\                                                                                           /     3\               3                                        /     3\                /     3\         \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            //       3\                /     3\                                                                                           /     3\               3                                        /     3\                /     3\         \                                                                                                   /                                                  /     3\         \ /                                                      /     3\               3                                      /     3\                /     3\         \     /                                                              /     3\         \ //       3\                /     3\                                                                                           /     3\               3                                        /     3\                /     3\         \                                                                                    2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \
                           |    /                                                  /     3\         \     |  \1 + 4*x /*sin(2*x) + 2*x*\1 + x /*cos(2*x)       2                            2*\\1 + x /*cos(2*x) + \1 + 4*x /*cos(2*x) + 3*x *cos(2*x) + 6*x *sin(2*x) - 2*x*\1 + x /*sin(2*x)/     /       3\              /     3\                3            6*x *sin(2*x)   2*\1 + x /*sin(2*x)   2*\1 + x /*cos(2*x)       /     3\            6*x *sin(2*x)   6*x *cos(2*x)   4*x*\1 + x /*cos(2*x)   2*x*\1 + x /*sin(2*x)   3*x*\1 + x /*sin(2*x)|     /                                                  /     3\         \     |\1 + 4*x /*sin(2*x) + 2*x*\1 + x /*cos(2*x)       2               3              /     3\              /       3\            \1 + x /*sin(2*x)   3*x *sin(2*x)       /     3\            2*x*\1 + x /*sin(2*x)   2*x*\1 + x /*cos(2*x)|        /                                                  /     3\         \       |\1 + 4*x /*sin(2*x) + 2*x*\1 + x /*cos(2*x)       2               3              /     3\              /       3\            \1 + x /*sin(2*x)   3*x *sin(2*x)       /     3\            2*x*\1 + x /*sin(2*x)   2*x*\1 + x /*cos(2*x)|     |\1 + 4*x /*sin(2*x) + 2*x*\1 + x /*cos(2*x)       2               3              /     3\              /       3\            \1 + x /*sin(2*x)   3*x *sin(2*x)       /     3\            2*x*\1 + x /*sin(2*x)   2*x*\1 + x /*cos(2*x)|     /                                                  /     3\         \   /                                                  /     3\         \ /                                                              /     3\         \       /                                                  /     3\         \               /                                                  /     3\         \     /                                                  /     3\         \              |\1 + 4*x /*sin(2*x) + 2*x*\1 + x /*cos(2*x)       2               3              /     3\              /       3\            \1 + x /*sin(2*x)   3*x *sin(2*x)       /     3\            2*x*\1 + x /*sin(2*x)   2*x*\1 + x /*cos(2*x)|                /                                                  /     3\         \              |  /       3\                /     3\            x*\1 + x /*sin(2*x)| |  /     3\               2               3            \1 + x /*sin(2*x)   3*x *sin(2*x)       /     3\            x*\1 + x /*sin(2*x)   2*x*\1 + x /*cos(2*x)|     |/     3\               3                /     3\            x*\1 + x /*sin(2*x)| |\1 + 4*x /*sin(2*x) + 2*x*\1 + x /*cos(2*x)       2               3              /     3\              /       3\            \1 + x /*sin(2*x)   3*x *sin(2*x)       /     3\            2*x*\1 + x /*sin(2*x)   2*x*\1 + x /*cos(2*x)|   /                                                              /     3\         \  /                                                  /     3\         \   /                                                  /     3\         \ /                                                              /     3\         \     /                                                  /     3\         \            /                                                  /     3\         \ /                                                              /     3\         \     /                                                  /     3\         \ /                                                              /     3\         \         |
     _____________________ |    |  /       3\                /     3\            x*\1 + x /*sin(2*x)|   2*|- ------------------------------------------- - 36*x *cos(2*x) - 12*x*sin(2*x) + --------------------------------------------------------------------------------------------------- + 2*\1 + 4*x /*sin(2*x) + 4*\1 + x /*sin(2*x) + 12*x *sin(2*x) - ------------- - ------------------- + ------------------- + 4*x*\1 + x /*cos(2*x) + ------------- + ------------- - --------------------- - --------------------- + ---------------------|     |  /       3\                /     3\            x*\1 + x /*sin(2*x)|   2*|------------------------------------------- - 12*x *sin(2*x) - 6*x *cos(2*x) - 2*\1 + x /*cos(2*x) - 2*\1 + 4*x /*cos(2*x) + ----------------- + ------------- + 4*x*\1 + x /*sin(2*x) - --------------------- + ---------------------|      3 |  /       3\                /     3\            x*\1 + x /*sin(2*x)|   2*x*|------------------------------------------- - 12*x *sin(2*x) - 6*x *cos(2*x) - 2*\1 + x /*cos(2*x) - 2*\1 + 4*x /*cos(2*x) + ----------------- + ------------- + 4*x*\1 + x /*sin(2*x) - --------------------- + ---------------------|   2*|------------------------------------------- - 12*x *sin(2*x) - 6*x *cos(2*x) - 2*\1 + x /*cos(2*x) - 2*\1 + 4*x /*cos(2*x) + ----------------- + ------------- + 4*x*\1 + x /*sin(2*x) - --------------------- + ---------------------|     |  /       3\                /     3\            x*\1 + x /*sin(2*x)|   |  /       3\                /     3\            x*\1 + x /*sin(2*x)| |/     3\               3                /     3\            x*\1 + x /*sin(2*x)|       |  /       3\                /     3\            x*\1 + x /*sin(2*x)|        2      |  /       3\                /     3\            x*\1 + x /*sin(2*x)|     |  /       3\                /     3\            x*\1 + x /*sin(2*x)|            4*|------------------------------------------- - 12*x *sin(2*x) - 6*x *cos(2*x) - 2*\1 + x /*cos(2*x) - 2*\1 + 4*x /*cos(2*x) + ----------------- + ------------- + 4*x*\1 + x /*sin(2*x) - --------------------- + ---------------------|*cos(2*x)       |  /       3\                /     3\            x*\1 + x /*sin(2*x)|            2*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*|2*\1 + x /*cos(2*x) + 6*x *sin(2*x) + 6*x *cos(2*x) - ----------------- - ------------- - 2*x*\1 + x /*sin(2*x) + ------------------- - ---------------------|   2*|\1 + x /*sin(2*x) + 3*x *sin(2*x) + 2*x*\1 + x /*cos(2*x) - -------------------|*|------------------------------------------- - 12*x *sin(2*x) - 6*x *cos(2*x) - 2*\1 + x /*cos(2*x) - 2*\1 + 4*x /*cos(2*x) + ----------------- + ------------- + 4*x*\1 + x /*sin(2*x) - --------------------- + ---------------------|   |/     3\               3                /     3\            x*\1 + x /*sin(2*x)|  |  /       3\                /     3\            x*\1 + x /*sin(2*x)|   |  /       3\                /     3\            x*\1 + x /*sin(2*x)| |/     3\               3                /     3\            x*\1 + x /*sin(2*x)|     |  /       3\                /     3\            x*\1 + x /*sin(2*x)|            |  /       3\                /     3\            x*\1 + x /*sin(2*x)| |/     3\               3                /     3\            x*\1 + x /*sin(2*x)|     |  /       3\                /     3\            x*\1 + x /*sin(2*x)| |/     3\               3                /     3\            x*\1 + x /*sin(2*x)|         |
    /   /     3\           |  4*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|     |                           2                                                                                                    -2 + x                                                                                                                          2                  2               -2 + x                                     -2 + x          -2 + x                    2                 -2 + x                        3      |   2*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|     |                   -2 + x                                                                                                          -2 + x            -2 + x                                            2                 -2 + x       |   6*x *|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|       |                   -2 + x                                                                                                          -2 + x            -2 + x                                            2                 -2 + x       |     |                   -2 + x                                                                                                          -2 + x            -2 + x                                            2                 -2 + x       |   2*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|   |- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*|\1 + x /*sin(2*x) + 3*x *sin(2*x) + 2*x*\1 + x /*cos(2*x) - -------------------|   2*x*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|   8*cos (2*x)*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|   4*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*cos(2*x)     |                   -2 + x                                                                                                          -2 + x            -2 + x                                            2                 -2 + x       |            4*x*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*cos(2*x)     \                                                       -2 + x      / |                                                            -2 + x            -2 + x                                           2                -2 + x       |     \                                                                   -2 + x      / |                   -2 + x                                                                                                          -2 + x            -2 + x                                            2                 -2 + x       |   |\1 + x /*sin(2*x) + 3*x *sin(2*x) + 2*x*\1 + x /*cos(2*x) - -------------------| *|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|   |- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*|\1 + x /*sin(2*x) + 3*x *sin(2*x) + 2*x*\1 + x /*cos(2*x) - -------------------|   4*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*cos(2*x)   |- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*|\1 + x /*sin(2*x) + 3*x *sin(2*x) + 2*x*\1 + x /*cos(2*x) - -------------------|   2*|- \1 + 4*x /*sin(2*x) - 2*x*\1 + x /*cos(2*x) + -------------------|*|\1 + x /*sin(2*x) + 3*x *sin(2*x) + 2*x*\1 + x /*cos(2*x) - -------------------|*cos(2*x)|
   /  x*\1 + x /*sin(2*x)  |    \                                                       -2 + x      /     \                   (-2 + x)                                                                                                                                                                                                                             (-2 + x)           (-2 + x)                                                                                             (-2 + x)                                        (-2 + x)       /     \                                                       -2 + x      /     \                                                                                                                                                                                               (-2 + x)                               /        \                                                       -2 + x      /       \                                                                                                                                                                                               (-2 + x)                               /     \                                                                                                                                                                                               (-2 + x)                               /     \                                                       -2 + x      /   \                                                       -2 + x      / \                                                                   -2 + x      /       \                                                       -2 + x      /               \                                                       -2 + x      /     \                                                       -2 + x      /              \                                                                                                                                                                                               (-2 + x)                               /                \                                                       -2 + x      /                                                                                    \                                                                                                                       (-2 + x)                              /                                                                                       \                                                                                                                                                                                               (-2 + x)                               /   \                                                                   -2 + x      /  \                                                       -2 + x      /   \                                                       -2 + x      / \                                                                   -2 + x      /     \                                                       -2 + x      /            \                                                       -2 + x      / \                                                                   -2 + x      /     \                                                       -2 + x      / \                                                                   -2 + x      /         |
3 /   ------------------- *|- ----------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------- - --------------------------------------------------------------------------------- - -------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\/           -2 + x        |                                    3*x                                                                                                                                                                                                                                                             3*x                                                                                                                                                                                                                                                                3                                                                                                                                                          2                                                                                                                                                              2                                                                                                                                                            3                                                                                                                                                                                                                                     3*x*(-2 + x)                                                                                                                                                  2                                                                                                                    2                                                                                                          /     3\                                                                                 2                                                                              2                                                                                                                                                                  3*x*sin(2*x)                                                                                                                                                      /     3\                                                                                                                                                         2 /     3\                                                                                                                                                                                                                                                                          2 /     3\                                                                                                                                                                                                                                            2                                                                                                                                                 3 /     3\                                                                                                         3*x*(-2 + x)*sin(2*x)                                                                                                2 /     3\                                                                                                                                                         2 /     3\    2                                                                           |
                           |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    3*x                                                                                                                                                        3*x                                                                                                                                                       /     3\                                                                                                                                                        1 + x                                                                                                                                                                                                                                                                                                                                                                                                 3*x *(-2 + x)                                                                                                   /     3\                                                                                                           \1 + x /*(-2 + x)                                                                 3*x*sin (2*x)                                                                      3*x *sin(2*x)                                                                                                                                                                                                                                                                                                                           \1 + x /*sin(2*x)                                                                                                                                             9*x *\1 + x /*sin(2*x)                                                                                                                                                                                                                                                              9*x *\1 + x /*sin(2*x)                                                                                                                                                                                                                         3 /     3\     2                                                                                                                                         3*x *\1 + x /*sin(2*x)                                                                                                                                                                                                                  3*x *\1 + x /*(-2 + x)*sin(2*x)                                                                                                                                    3*x *\1 + x /*sin (2*x)                                                                      |
                           \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \1 + x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \1 + x / *sin(2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           27*x *\1 + x / *sin (2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            /
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$$\frac{\sqrt[3]{\frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}} \left(- \frac{6 x^{3} \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{\left(x^{3} + 1\right)^{2}} - \frac{4 x \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \cos{\left(2 x \right)}}{\left(x^{3} + 1\right) \sin{\left(2 x \right)}} + \frac{2 x \left(- 6 x^{3} \cos{\left(2 x \right)} + \frac{3 x^{3} \sin{\left(2 x \right)}}{x - 2} - 12 x^{2} \sin{\left(2 x \right)} + 4 x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{x - 2} - \frac{2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} - 2 \left(x^{3} + 1\right) \cos{\left(2 x \right)} - 2 \left(4 x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{\left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)}{x^{3} + 1} + \frac{2 x \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{\left(x - 2\right) \left(x^{3} + 1\right)} + \frac{\left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} - \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{\left(x^{3} + 1\right)^{2} \sin{\left(2 x \right)}} - \frac{4 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 x} - \frac{8 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \cos^{2}{\left(2 x \right)}}{3 x \sin^{2}{\left(2 x \right)}} + \frac{4 \left(- 6 x^{3} \cos{\left(2 x \right)} + \frac{3 x^{3} \sin{\left(2 x \right)}}{x - 2} - 12 x^{2} \sin{\left(2 x \right)} + 4 x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{x - 2} - \frac{2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} - 2 \left(x^{3} + 1\right) \cos{\left(2 x \right)} - 2 \left(4 x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{\left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right) \cos{\left(2 x \right)}}{3 x \sin{\left(2 x \right)}} - \frac{2 \left(12 x^{3} \sin{\left(2 x \right)} + \frac{6 x^{3} \cos{\left(2 x \right)}}{x - 2} - \frac{6 x^{3} \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} - 36 x^{2} \cos{\left(2 x \right)} + \frac{6 x^{2} \sin{\left(2 x \right)}}{x - 2} + 4 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} - 12 x \sin{\left(2 x \right)} - \frac{2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \frac{4 x \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{\left(x - 2\right)^{2}} + \frac{3 x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{3}} + 4 \left(x^{3} + 1\right) \sin{\left(2 x \right)} + 2 \left(4 x^{3} + 1\right) \sin{\left(2 x \right)} + \frac{2 \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{x - 2} + \frac{2 \left(3 x^{3} \cos{\left(2 x \right)} + 6 x^{2} \sin{\left(2 x \right)} - 2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \cos{\left(2 x \right)}\right)}{x - 2} - \frac{2 \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} - \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}}\right)}{3 x} + \frac{4 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \cos{\left(2 x \right)}}{3 x \left(x - 2\right) \sin{\left(2 x \right)}} - \frac{2 \left(- 6 x^{3} \cos{\left(2 x \right)} + \frac{3 x^{3} \sin{\left(2 x \right)}}{x - 2} - 12 x^{2} \sin{\left(2 x \right)} + 4 x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{x - 2} - \frac{2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} - 2 \left(x^{3} + 1\right) \cos{\left(2 x \right)} - 2 \left(4 x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{\left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)}{3 x \left(x - 2\right)} - \frac{4 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \cos{\left(2 x \right)}}{3 x^{2} \sin{\left(2 x \right)}} + \frac{2 \left(- 6 x^{3} \cos{\left(2 x \right)} + \frac{3 x^{3} \sin{\left(2 x \right)}}{x - 2} - 12 x^{2} \sin{\left(2 x \right)} + 4 x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{x - 2} - \frac{2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} - 2 \left(x^{3} + 1\right) \cos{\left(2 x \right)} - 2 \left(4 x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{\left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)}{3 x^{2}} + \frac{2 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} - \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right) \cos{\left(2 x \right)}}{3 x^{2} \left(x^{3} + 1\right) \sin^{2}{\left(2 x \right)}} - \frac{2 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \left(6 x^{3} \cos{\left(2 x \right)} - \frac{3 x^{3} \sin{\left(2 x \right)}}{x - 2} + 6 x^{2} \sin{\left(2 x \right)} - 2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)} - \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{x - 2} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} + 2 \left(x^{3} + 1\right) \cos{\left(2 x \right)} - \frac{\left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)}{9 x^{2} \left(x^{3} + 1\right) \sin{\left(2 x \right)}} - \frac{2 \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} - \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right) \left(- 6 x^{3} \cos{\left(2 x \right)} + \frac{3 x^{3} \sin{\left(2 x \right)}}{x - 2} - 12 x^{2} \sin{\left(2 x \right)} + 4 x \left(x^{3} + 1\right) \sin{\left(2 x \right)} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)}}{x - 2} - \frac{2 x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{\left(x - 2\right)^{2}} - 2 \left(x^{3} + 1\right) \cos{\left(2 x \right)} - 2 \left(4 x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{\left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \frac{2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2}\right)}{9 x^{2} \left(x^{3} + 1\right) \sin{\left(2 x \right)}} + \frac{2 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 x^{2} \left(x - 2\right)} - \frac{\left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} - \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 x^{2} \left(x - 2\right) \left(x^{3} + 1\right) \sin{\left(2 x \right)}} - \frac{2 \left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 x^{3}} + \frac{\left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} - \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)}{3 x^{3} \left(x^{3} + 1\right) \sin{\left(2 x \right)}} - \frac{\left(- 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} + \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} - \left(4 x^{3} + 1\right) \sin{\left(2 x \right)}\right) \left(3 x^{3} \sin{\left(2 x \right)} + 2 x \left(x^{3} + 1\right) \cos{\left(2 x \right)} - \frac{x \left(x^{3} + 1\right) \sin{\left(2 x \right)}}{x - 2} + \left(x^{3} + 1\right) \sin{\left(2 x \right)}\right)^{2}}{27 x^{3} \left(x^{3} + 1\right)^{2} \sin^{2}{\left(2 x \right)}}\right)}{\left(x^{3} + 1\right) \sin{\left(2 x \right)}}$$

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Derivada de ((x*(x^3+1)*sin2x)/(x-2))^(1/3)

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Derivada de ((x(x^3+1)sin2x)/(x-2))^(1/3)

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Derivada de ((x*(x^3+1)*sin2x)/(x-2))^(1/3)

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Derivada de ((x(x^3+1)sin2x)/(x-2))^(1/3)