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y=(sin4x)^(sin4x)
Derivada de la función/ sin4x/ y=(sin4x)^(sin4x)

Derivada de y=(sin4x)^(sin4x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   sin(4*x)     
sin        (4*x)
$$\sin^{\sin{\left(4 x \right)}}{\left(4 x \right)}$$ 
sin(4*x)^sin(4*x)
Solución detallada

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

    Perola derivada

Respuesta:

Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   sin(4*x)                                             
sin        (4*x)*(4*cos(4*x) + 4*cos(4*x)*log(sin(4*x)))
$$\left(4 \log{\left(\sin{\left(4 x \right)} \right)} \cos{\left(4 x \right)} + 4 \cos{\left(4 x \right)}\right) \sin^{\sin{\left(4 x \right)}}{\left(4 x \right)}$$
Simplificar
Segunda derivada [src] 
                    /                                                2                              \
      sin(4*x)      |                               2    2        cos (4*x)                         |
16*sin        (4*x)*|-sin(4*x) + (1 + log(sin(4*x))) *cos (4*x) + --------- - log(sin(4*x))*sin(4*x)|
                    \                                              sin(4*x)                         /
$$16 \left(\left(\log{\left(\sin{\left(4 x \right)} \right)} + 1\right)^{2} \cos^{2}{\left(4 x \right)} - \log{\left(\sin{\left(4 x \right)} \right)} \sin{\left(4 x \right)} - \sin{\left(4 x \right)} + \frac{\cos^{2}{\left(4 x \right)}}{\sin{\left(4 x \right)}}\right) \sin^{\sin{\left(4 x \right)}}{\left(4 x \right)}$$
Simplificar
Tercera derivada [src] 
                    /                                                         2                              /                            2                \\         
      sin(4*x)      |                                        3    2        cos (4*x)                         |                         cos (4*x)           ||         
64*sin        (4*x)*|-4 - log(sin(4*x)) + (1 + log(sin(4*x))) *cos (4*x) - --------- - 3*(1 + log(sin(4*x)))*|log(sin(4*x))*sin(4*x) - --------- + sin(4*x)||*cos(4*x)
                    |                                                         2                              \                          sin(4*x)           /|         
                    \                                                      sin (4*x)                                                                        /
$$64 \left(\left(\log{\left(\sin{\left(4 x \right)} \right)} + 1\right)^{3} \cos^{2}{\left(4 x \right)} - 3 \left(\log{\left(\sin{\left(4 x \right)} \right)} + 1\right) \left(\log{\left(\sin{\left(4 x \right)} \right)} \sin{\left(4 x \right)} + \sin{\left(4 x \right)} - \frac{\cos^{2}{\left(4 x \right)}}{\sin{\left(4 x \right)}}\right) - \log{\left(\sin{\left(4 x \right)} \right)} - 4 - \frac{\cos^{2}{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}}\right) \sin^{\sin{\left(4 x \right)}}{\left(4 x \right)} \cos{\left(4 x \right)}$$
Simplificar
Gráfico
Derivada de y=(sin4x)^(sin4x)
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