Derivada de y=(sin5x)^(e^x)

Ha introducido [src]

          / x\
          \E /
(sin(5*x))

$$\sin^{e^{x}}{\left(5 x \right)}$$

sin(5*x)^(E^x)

Solución detallada

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Perola derivada

$\left(\log{\left(e^{x} \right)} + 1\right) e^{x e^{x}}$
Simplificamos:

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

          / x\ /                               x\
          \E / | x                 5*cos(5*x)*e |
(sin(5*x))    *|e *log(sin(5*x)) + -------------|
               \                      sin(5*x)  /

$$\left(e^{x} \log{\left(\sin{\left(5 x \right)} \right)} + \frac{5 e^{x} \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right) \sin^{e^{x}}{\left(5 x \right)}$$

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Segunda derivada [src]

          / x\ /                                  2            2                                   \   
          \e / |      /5*cos(5*x)                \   x   25*cos (5*x)   10*cos(5*x)                |  x
(sin(5*x))    *|-25 + |---------- + log(sin(5*x))| *e  - ------------ + ----------- + log(sin(5*x))|*e 
               |      \ sin(5*x)                 /           2            sin(5*x)                 |   
               \                                          sin (5*x)                                /

$$\left(\left(\log{\left(\sin{\left(5 x \right)} \right)} + \frac{5 \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right)^{2} e^{x} + \log{\left(\sin{\left(5 x \right)} \right)} - 25 + \frac{10 \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} - \frac{25 \cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}}\right) e^{x} \sin^{e^{x}}{\left(5 x \right)}$$

Simplificar

Tercera derivada [src]

          / x\ /                                  3              2               3                                                      /            2                                   \                   \   
          \e / |      /5*cos(5*x)                \   2*x   75*cos (5*x)   250*cos (5*x)   265*cos(5*x)     /5*cos(5*x)                \ |      25*cos (5*x)   10*cos(5*x)                |  x                |  x
(sin(5*x))    *|-75 + |---------- + log(sin(5*x))| *e    - ------------ + ------------- + ------------ + 3*|---------- + log(sin(5*x))|*|-25 - ------------ + ----------- + log(sin(5*x))|*e  + log(sin(5*x))|*e 
               |      \ sin(5*x)                 /             2               3            sin(5*x)       \ sin(5*x)                 / |          2            sin(5*x)                 |                   |   
               \                                            sin (5*x)       sin (5*x)                                                   \       sin (5*x)                                /                   /

$$\left(\left(\log{\left(\sin{\left(5 x \right)} \right)} + \frac{5 \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right)^{3} e^{2 x} + 3 \left(\log{\left(\sin{\left(5 x \right)} \right)} + \frac{5 \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}}\right) \left(\log{\left(\sin{\left(5 x \right)} \right)} - 25 + \frac{10 \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} - \frac{25 \cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}}\right) e^{x} + \log{\left(\sin{\left(5 x \right)} \right)} - 75 + \frac{265 \cos{\left(5 x \right)}}{\sin{\left(5 x \right)}} - \frac{75 \cos^{2}{\left(5 x \right)}}{\sin^{2}{\left(5 x \right)}} + \frac{250 \cos^{3}{\left(5 x \right)}}{\sin^{3}{\left(5 x \right)}}\right) e^{x} \sin^{e^{x}}{\left(5 x \right)}$$

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Gráfico

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Expresiones idénticas

Derivada de y=(sin5x)^(e^x)

Gráfico:

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Solución