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

Derivada de y=(sinhx)^(x)

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

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Solución

Ha introducido [src] 
    x   
sinh (x)
$$\sinh^{x}{\left(x \right)}$$ 
sinh(x)^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] 
    x    /x*cosh(x)               \
sinh (x)*|--------- + log(sinh(x))|
         \ sinh(x)                /
$$\left(\frac{x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + \log{\left(\sinh{\left(x \right)} \right)}\right) \sinh^{x}{\left(x \right)}$$
Simplificar
Segunda derivada [src] 
         /                              2                     2   \
    x    |    /x*cosh(x)               \    2*cosh(x)   x*cosh (x)|
sinh (x)*|x + |--------- + log(sinh(x))|  + --------- - ----------|
         |    \ sinh(x)                /     sinh(x)         2    |
         \                                               sinh (x) /
$$\left(x - \frac{x \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}} + \left(\frac{x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + \log{\left(\sinh{\left(x \right)} \right)}\right)^{2} + \frac{2 \cosh{\left(x \right)}}{\sinh{\left(x \right)}}\right) \sinh^{x}{\left(x \right)}$$
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Tercera derivada [src] 
         /                              3         2                                   /                      2   \                         3   \
    x    |    /x*cosh(x)               \    3*cosh (x)     /x*cosh(x)               \ |    2*cosh(x)   x*cosh (x)|   2*x*cosh(x)   2*x*cosh (x)|
sinh (x)*|3 + |--------- + log(sinh(x))|  - ---------- + 3*|--------- + log(sinh(x))|*|x + --------- - ----------| - ----------- + ------------|
         |    \ sinh(x)                /         2         \ sinh(x)                / |     sinh(x)         2    |     sinh(x)           3     |
         \                                   sinh (x)                                 \                 sinh (x) /                   sinh (x)  /
$$\left(- \frac{2 x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + \frac{2 x \cosh^{3}{\left(x \right)}}{\sinh^{3}{\left(x \right)}} + \left(\frac{x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + \log{\left(\sinh{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{x \cosh{\left(x \right)}}{\sinh{\left(x \right)}} + \log{\left(\sinh{\left(x \right)} \right)}\right) \left(x - \frac{x \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}} + \frac{2 \cosh{\left(x \right)}}{\sinh{\left(x \right)}}\right) + 3 - \frac{3 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) \sinh^{x}{\left(x \right)}$$
Simplificar
Gráfico
Derivada de y=(sinhx)^(x)
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