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(x*sin(4x))^(2x)
(x multiplicar por seno de (4x)) en el grado (2x)
(x*sin(4x))(2x)
x*sin4x2x
(xsin(4x))^(2x)
(xsin(4x))(2x)
xsin4x2x
xsin4x^2x
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Derivada de la función/ x*sin/ sin(4x)/ (x*sin(4x))^(2x)

Derivada de (x*sin(4x))^(2x)

Solución

Ha introducido [src]

            2*x
(x*sin(4*x))

\left(x \sin{\left(4 x \right)}\right)^{2 x}

(x*sin(4*x))^(2*x)

Solución detallada

No logro encontrar los pasos en la búsqueda de esta derivada.

Perola derivada

$\left(2 x\right)^{2 x} \left(\log{\left(2 x \right)} + 1\right)$

Respuesta:

$\left(2 x\right)^{2 x} \left(\log{\left(2 x \right)} + 1\right)$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

            2*x /                    2*(4*x*cos(4*x) + sin(4*x))\
(x*sin(4*x))   *|2*log(x*sin(4*x)) + ---------------------------|
                \                              sin(4*x)         /

\left(x \sin{\left(4 x \right)}\right)^{2 x} \left(\frac{2 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right)}{\sin{\left(4 x \right)}} + 2 \log{\left(x \sin{\left(4 x \right)} \right)}\right)

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Segunda derivada [src]

                  /                                                               4*x*cos(4*x) + sin(4*x)                   4*(4*x*cos(4*x) + sin(4*x))*cos(4*x)\
                  |                                             2   -8*cos(4*x) - ----------------------- + 16*x*sin(4*x) + ------------------------------------|
              2*x |  /4*x*cos(4*x) + sin(4*x)                  \                             x                                            sin(4*x)              |
2*(x*sin(4*x))   *|2*|----------------------- + log(x*sin(4*x))|  - --------------------------------------------------------------------------------------------|
                  \  \        sin(4*x)                         /                                              sin(4*x)                                          /

2 \left(x \sin{\left(4 x \right)}\right)^{2 x} \left(2 \left(\frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{\sin{\left(4 x \right)}} + \log{\left(x \sin{\left(4 x \right)} \right)}\right)^{2} - \frac{16 x \sin{\left(4 x \right)} + \frac{4 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - 8 \cos{\left(4 x \right)} - \frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{x}}{\sin{\left(4 x \right)}}\right)

Simplificar

Tercera derivada [src]

                  /                                                                                                                                                                       2                                                                                                                                                                                                                     \
                  |                                                               4*x*cos(4*x) + sin(4*x)   8*(-cos(4*x) + 2*x*sin(4*x))   64*(-cos(4*x) + 2*x*sin(4*x))*cos(4*x)   32*cos (4*x)*(4*x*cos(4*x) + sin(4*x))   4*(4*x*cos(4*x) + sin(4*x))*cos(4*x)                                                                                                                                               |
                  |                                                 32*sin(4*x) + ----------------------- + ---------------------------- - -------------------------------------- - -------------------------------------- + ------------------------------------     /4*x*cos(4*x) + sin(4*x)                  \ /              4*x*cos(4*x) + sin(4*x)                   4*(4*x*cos(4*x) + sin(4*x))*cos(4*x)\|
                  |                                             3                             2                          x                                sin(4*x)                                   2                                    x*sin(4*x)                6*|----------------------- + log(x*sin(4*x))|*|-8*cos(4*x) - ----------------------- + 16*x*sin(4*x) + ------------------------------------||
              2*x |  /4*x*cos(4*x) + sin(4*x)                  \                             x                                                                                                    sin (4*x)                                                           \        sin(4*x)                         / \                         x                                            sin(4*x)              /|
2*(x*sin(4*x))   *|4*|----------------------- + log(x*sin(4*x))|  - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------|
                  \  \        sin(4*x)                         /                                                                                               sin(4*x)                                                                                                                                                               sin(4*x)                                                                  /

2 \left(x \sin{\left(4 x \right)}\right)^{2 x} \left(4 \left(\frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{\sin{\left(4 x \right)}} + \log{\left(x \sin{\left(4 x \right)} \right)}\right)^{3} - \frac{6 \left(\frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{\sin{\left(4 x \right)}} + \log{\left(x \sin{\left(4 x \right)} \right)}\right) \left(16 x \sin{\left(4 x \right)} + \frac{4 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - 8 \cos{\left(4 x \right)} - \frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{x}\right)}{\sin{\left(4 x \right)}} - \frac{- \frac{64 \left(2 x \sin{\left(4 x \right)} - \cos{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - \frac{32 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos^{2}{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}} + 32 \sin{\left(4 x \right)} + \frac{8 \left(2 x \sin{\left(4 x \right)} - \cos{\left(4 x \right)}\right)}{x} + \frac{4 \left(4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}}{x \sin{\left(4 x \right)}} + \frac{4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{x^{2}}}{\sin{\left(4 x \right)}}\right)

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Gráfico

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Derivada de (x*sin(4x))^(2x)

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