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y=(sin9x)^x^2
Derivada de la función/ sin9x/ y=(sin9x)^x^2

Derivada de y=(sin9x)^x^2

Función f() - derivada -er orden en el punto
v

Gráfico:

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Solución

Ha introducido [src] 
          / 2\
          \x /
(sin(9*x))
$$\sin^{x^{2}}{\left(9 x \right)}$$ 
sin(9*x)^(x^2)
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] 
          / 2\ /                       2         \
          \x / |                    9*x *cos(9*x)|
(sin(9*x))    *|2*x*log(sin(9*x)) + -------------|
               \                       sin(9*x)  /
$$\left(\frac{9 x^{2} \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}} + 2 x \log{\left(\sin{\left(9 x \right)} \right)}\right) \sin^{x^{2}}{\left(9 x \right)}$$
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Segunda derivada [src] 
          / 2\ /                                                               2       2    2                     \
          \x / |      2                      2 /                  9*x*cos(9*x)\    81*x *cos (9*x)   36*x*cos(9*x)|
(sin(9*x))    *|- 81*x  + 2*log(sin(9*x)) + x *|2*log(sin(9*x)) + ------------|  - --------------- + -------------|
               |                               \                    sin(9*x)  /          2              sin(9*x)  |
               \                                                                      sin (9*x)                   /
$$\left(x^{2} \left(\frac{9 x \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}} + 2 \log{\left(\sin{\left(9 x \right)} \right)}\right)^{2} - 81 x^{2} - \frac{81 x^{2} \cos^{2}{\left(9 x \right)}}{\sin^{2}{\left(9 x \right)}} + \frac{36 x \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}} + 2 \log{\left(\sin{\left(9 x \right)} \right)}\right) \sin^{x^{2}}{\left(9 x \right)}$$
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Tercera derivada [src] 
          / 2\ /                                            3                          2                                             /                                               2    2     \         2    3              2         \
          \x / |          3 /                  9*x*cos(9*x)\    54*cos(9*x)   486*x*cos (9*x)       /                  9*x*cos(9*x)\ |                       2   36*x*cos(9*x)   81*x *cos (9*x)|   1458*x *cos (9*x)   1458*x *cos(9*x)|
(sin(9*x))    *|-486*x + x *|2*log(sin(9*x)) + ------------|  + ----------- - --------------- - 3*x*|2*log(sin(9*x)) + ------------|*|-2*log(sin(9*x)) + 81*x  - ------------- + ---------------| + ----------------- + ----------------|
               |            \                    sin(9*x)  /      sin(9*x)          2               \                    sin(9*x)  / |                              sin(9*x)           2        |          3                sin(9*x)    |
               \                                                                 sin (9*x)                                           \                                              sin (9*x)   /       sin (9*x)                       /
$$\left(x^{3} \left(\frac{9 x \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}} + 2 \log{\left(\sin{\left(9 x \right)} \right)}\right)^{3} + \frac{1458 x^{2} \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}} + \frac{1458 x^{2} \cos^{3}{\left(9 x \right)}}{\sin^{3}{\left(9 x \right)}} - 3 x \left(\frac{9 x \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}} + 2 \log{\left(\sin{\left(9 x \right)} \right)}\right) \left(81 x^{2} + \frac{81 x^{2} \cos^{2}{\left(9 x \right)}}{\sin^{2}{\left(9 x \right)}} - \frac{36 x \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}} - 2 \log{\left(\sin{\left(9 x \right)} \right)}\right) - 486 x - \frac{486 x \cos^{2}{\left(9 x \right)}}{\sin^{2}{\left(9 x \right)}} + \frac{54 \cos{\left(9 x \right)}}{\sin{\left(9 x \right)}}\right) \sin^{x^{2}}{\left(9 x \right)}$$
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Gráfico
Derivada de y=(sin9x)^x^2
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