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

Ha introducido [src]

        / x\
        \E /
(sin(x))

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

sin(x)^(E^x)

Solución detallada

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

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

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

Simplificar

Segunda derivada [src]

        / x\ /                           2         2                            \   
        \e / |     /cos(x)              \   x   cos (x)   2*cos(x)              |  x
(sin(x))    *|-1 + |------ + log(sin(x))| *e  - ------- + -------- + log(sin(x))|*e 
             |     \sin(x)              /          2       sin(x)               |   
             \                                  sin (x)                         /

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

Simplificar

Tercera derivada [src]

        / x\ /                           3             2           3                                          /        2                            \                 \   
        \e / |     /cos(x)              \   2*x   3*cos (x)   2*cos (x)   5*cos(x)     /cos(x)              \ |     cos (x)   2*cos(x)              |  x              |  x
(sin(x))    *|-3 + |------ + log(sin(x))| *e    - --------- + --------- + -------- + 3*|------ + log(sin(x))|*|-1 - ------- + -------- + log(sin(x))|*e  + log(sin(x))|*e 
             |     \sin(x)              /             2           3        sin(x)      \sin(x)              / |        2       sin(x)               |                 |   
             \                                     sin (x)     sin (x)                                        \     sin (x)                         /                 /

$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} e^{2 x} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\log{\left(\sin{\left(x \right)} \right)} - 1 + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) e^{x} + \log{\left(\sin{\left(x \right)} \right)} - 3 + \frac{5 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) e^{x} \sin^{e^{x}}{\left(x \right)}$$

Simplificar

Gráfico

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

Gráfico:

Definida a trozos:

Solución