Derivada de y=sinx^sinx

Ha introducido [src]

   sin(x)   
sin      (x)

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

sin(x)^sin(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   sin(x)                                 
sin      (x)*(cos(x)*log(sin(x)) + cos(x))

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

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Derivada de y=sinx^sinx

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