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

Derivada de y=(sinhx)^(x^2)

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

Ha introducido [src] 
         / 2\
         \x /
(sinh(x))
$$\sinh^{x^{2}}{\left(x \right)}$$ 
sinh(x)^(x^2)
Solución detallada

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

    Perola derivada

Respuesta:

Primera derivada [src] 
         / 2\ /                    2        \
         \x / |                   x *cosh(x)|
(sinh(x))    *|2*x*log(sinh(x)) + ----------|
              \                    sinh(x)  /
$$\left(\frac{x^{2} \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 x \log{\left(\sinh{\left(x \right)} \right)}\right) \sinh^{x^{2}}{\left(x \right)}$$
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Segunda derivada [src] 
         / 2\ /                                                     2    2     2                 \
         \x / | 2                     2 /                 x*cosh(x)\    x *cosh (x)   4*x*cosh(x)|
(sinh(x))    *|x  + 2*log(sinh(x)) + x *|2*log(sinh(x)) + ---------|  - ----------- + -----------|
              |                         \                  sinh(x) /          2         sinh(x)  |
              \                                                           sinh (x)               /
$$\left(x^{2} \left(\frac{x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 \log{\left(\sinh{\left(x \right)} \right)}\right)^{2} + x^{2} - \frac{x^{2} \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}} + \frac{4 x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 \log{\left(\sinh{\left(x \right)} \right)}\right) \sinh^{x^{2}}{\left(x \right)}$$
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Tercera derivada [src] 
         / 2\ /                                     3                       2         2              2     3                                       /                       2     2                 \\
         \x / |       3 /                 x*cosh(x)\    6*cosh(x)   6*x*cosh (x)   2*x *cosh(x)   2*x *cosh (x)       /                 x*cosh(x)\ | 2                    x *cosh (x)   4*x*cosh(x)||
(sinh(x))    *|6*x + x *|2*log(sinh(x)) + ---------|  + --------- - ------------ - ------------ + ------------- + 3*x*|2*log(sinh(x)) + ---------|*|x  + 2*log(sinh(x)) - ----------- + -----------||
              |         \                  sinh(x) /     sinh(x)          2          sinh(x)             3            \                  sinh(x) / |                            2         sinh(x)  ||
              \                                                       sinh (x)                       sinh (x)                                      \                        sinh (x)               //
$$\left(x^{3} \left(\frac{x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 \log{\left(\sinh{\left(x \right)} \right)}\right)^{3} - \frac{2 x^{2} \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + \frac{2 x^{2} \cosh^{3}{\left(x \right)}}{\sinh^{3}{\left(x \right)}} + 3 x \left(\frac{x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 \log{\left(\sinh{\left(x \right)} \right)}\right) \left(x^{2} - \frac{x^{2} \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}} + \frac{4 x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + 2 \log{\left(\sinh{\left(x \right)} \right)}\right) + 6 x - \frac{6 x \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}} + \frac{6 \cosh{\left(x \right)}}{\sinh{\left(x \right)}}\right) \sinh^{x^{2}}{\left(x \right)}$$
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