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Derivada de la función/ (x)^x/ y=sin/ sin(x)/ y=sin(x)^x^3

Derivada de y=sin(x)^x^3

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

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Solución

Ha introducido [src] 
        / 3\
        \x /
(sin(x))
$$\sin^{x^{3}}{\left(x \right)}$$ 
sin(x)^(x^3)
Solución detallada

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

    Perola derivada

Respuesta:

Primera derivada [src] 
        / 3\ /                    3       \
        \x / |   2               x *cos(x)|
(sin(x))    *|3*x *log(sin(x)) + ---------|
             \                     sin(x) /
$$\left(\frac{x^{3} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 3 x^{2} \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{x^{3}}{\left(x \right)}$$
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Segunda derivada [src] 
          / 3\ /                                                    2    2    2                \
          \x / |   2                    3 /                x*cos(x)\    x *cos (x)   6*x*cos(x)|
x*(sin(x))    *|- x  + 6*log(sin(x)) + x *|3*log(sin(x)) + --------|  - ---------- + ----------|
               |                          \                 sin(x) /        2          sin(x)  |
               \                                                         sin (x)               /
$$x \left(x^{3} \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 3 \log{\left(\sin{\left(x \right)} \right)}\right)^{2} - x^{2} - \frac{x^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{6 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 6 \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{x^{3}}{\left(x \right)}$$
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Tercera derivada [src] 
        / 3\ /                                                      3      2    2                                      /                      2    2                \      3    3         3                     \
        \x / |     2                    6 /                x*cos(x)\    9*x *cos (x)      3 /                x*cos(x)\ | 2                   x *cos (x)   6*x*cos(x)|   2*x *cos (x)   2*x *cos(x)   18*x*cos(x)|
(sin(x))    *|- 9*x  + 6*log(sin(x)) + x *|3*log(sin(x)) + --------|  - ------------ - 3*x *|3*log(sin(x)) + --------|*|x  - 6*log(sin(x)) + ---------- - ----------| + ------------ + ----------- + -----------|
             |                            \                 sin(x) /         2              \                 sin(x) / |                         2          sin(x)  |        3            sin(x)        sin(x)  |
             \                                                            sin (x)                                      \                      sin (x)               /     sin (x)                               /
$$\left(x^{6} \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 3 \log{\left(\sin{\left(x \right)} \right)}\right)^{3} - 3 x^{3} \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 3 \log{\left(\sin{\left(x \right)} \right)}\right) \left(x^{2} + \frac{x^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{6 x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 6 \log{\left(\sin{\left(x \right)} \right)}\right) + \frac{2 x^{3} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 x^{3} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 9 x^{2} - \frac{9 x^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{18 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 6 \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{x^{3}}{\left(x \right)}$$
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