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Derivada de y=(x-5)^(ch(x))

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Solución

Ha introducido [src]
       cosh(x)
(x - 5)       
$$\left(x - 5\right)^{\cosh{\left(x \right)}}$$
(x - 5)^cosh(x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Primera derivada [src]
       cosh(x) /cosh(x)                     \
(x - 5)       *|------- + log(x - 5)*sinh(x)|
               \ x - 5                      /
$$\left(x - 5\right)^{\cosh{\left(x \right)}} \left(\log{\left(x - 5 \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x - 5}\right)$$
Segunda derivada [src]
                /                               2                                              \
        cosh(x) |/cosh(x)                      \                           cosh(x)    2*sinh(x)|
(-5 + x)       *||------- + log(-5 + x)*sinh(x)|  + cosh(x)*log(-5 + x) - --------- + ---------|
                |\ -5 + x                      /                                  2     -5 + x |
                \                                                         (-5 + x)             /
$$\left(x - 5\right)^{\cosh{\left(x \right)}} \left(\left(\log{\left(x - 5 \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x - 5}\right)^{2} + \log{\left(x - 5 \right)} \cosh{\left(x \right)} + \frac{2 \sinh{\left(x \right)}}{x - 5} - \frac{\cosh{\left(x \right)}}{\left(x - 5\right)^{2}}\right)$$
Tercera derivada [src]
                /                               3                                                                                                                                            \
        cosh(x) |/cosh(x)                      \                          3*sinh(x)   2*cosh(x)   3*cosh(x)     /cosh(x)                      \ /                       cosh(x)    2*sinh(x)\|
(-5 + x)       *||------- + log(-5 + x)*sinh(x)|  + log(-5 + x)*sinh(x) - --------- + --------- + --------- + 3*|------- + log(-5 + x)*sinh(x)|*|cosh(x)*log(-5 + x) - --------- + ---------||
                |\ -5 + x                      /                                  2           3     -5 + x      \ -5 + x                      / |                              2     -5 + x ||
                \                                                         (-5 + x)    (-5 + x)                                                  \                      (-5 + x)             //
$$\left(x - 5\right)^{\cosh{\left(x \right)}} \left(\left(\log{\left(x - 5 \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x - 5}\right)^{3} + 3 \left(\log{\left(x - 5 \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x - 5}\right) \left(\log{\left(x - 5 \right)} \cosh{\left(x \right)} + \frac{2 \sinh{\left(x \right)}}{x - 5} - \frac{\cosh{\left(x \right)}}{\left(x - 5\right)^{2}}\right) + \log{\left(x - 5 \right)} \sinh{\left(x \right)} + \frac{3 \cosh{\left(x \right)}}{x - 5} - \frac{3 \sinh{\left(x \right)}}{\left(x - 5\right)^{2}} + \frac{2 \cosh{\left(x \right)}}{\left(x - 5\right)^{3}}\right)$$