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Derivada de la función/ x^sin/ sinhx/ y=x^sinhx

Derivada de y=x^sinhx

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

Ha introducido [src] 
 sinh(x)
x
xsinh⁡(x)x^{\sinh{\left(x \right)}} 
x^sinh(x)
Solución detallada

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

    Perola derivada

    (log⁡(sinh⁡(x))+1)sinh⁡sinh⁡(x)(x)\left(\log{\left(\sinh{\left(x \right)} \right)} + 1\right) \sinh^{\sinh{\left(x \right)}}{\left(x \right)}

Respuesta:

(log⁡(sinh⁡(x))+1)sinh⁡sinh⁡(x)(x)\left(\log{\left(\sinh{\left(x \right)} \right)} + 1\right) \sinh^{\sinh{\left(x \right)}}{\left(x \right)}

Primera derivada [src] 
 sinh(x) /sinh(x)                 \
x       *|------- + cosh(x)*log(x)|
         \   x                    /
xsinh⁡(x)(log⁡(x)cosh⁡(x)+sinh⁡(x)x)x^{\sinh{\left(x \right)}} \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right)
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Segunda derivada [src] 
         /                          2                                       \
 sinh(x) |/sinh(x)                 \                     sinh(x)   2*cosh(x)|
x       *||------- + cosh(x)*log(x)|  + log(x)*sinh(x) - ------- + ---------|
         |\   x                    /                         2         x    |
         \                                                  x               /
xsinh⁡(x)((log⁡(x)cosh⁡(x)+sinh⁡(x)x)2+log⁡(x)sinh⁡(x)+2cosh⁡(x)x−sinh⁡(x)x2)x^{\sinh{\left(x \right)}} \left(\left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right)^{2} + \log{\left(x \right)} \sinh{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{\sinh{\left(x \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
         /                          3                                                                                                                           \
 sinh(x) |/sinh(x)                 \                     3*cosh(x)   2*sinh(x)   3*sinh(x)     /sinh(x)                 \ /                 sinh(x)   2*cosh(x)\|
x       *||------- + cosh(x)*log(x)|  + cosh(x)*log(x) - --------- + --------- + --------- + 3*|------- + cosh(x)*log(x)|*|log(x)*sinh(x) - ------- + ---------||
         |\   x                    /                          2           3          x         \   x                    / |                     2         x    ||
         \                                                   x           x                                                \                    x               //
xsinh⁡(x)((log⁡(x)cosh⁡(x)+sinh⁡(x)x)3+3(log⁡(x)cosh⁡(x)+sinh⁡(x)x)(log⁡(x)sinh⁡(x)+2cosh⁡(x)x−sinh⁡(x)x2)+log⁡(x)cosh⁡(x)+3sinh⁡(x)x−3cosh⁡(x)x2+2sinh⁡(x)x3)x^{\sinh{\left(x \right)}} \left(\left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right)^{3} + 3 \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{2 \cosh{\left(x \right)}}{x} - \frac{\sinh{\left(x \right)}}{x^{2}}\right) + \log{\left(x \right)} \cosh{\left(x \right)} + \frac{3 \sinh{\left(x \right)}}{x} - \frac{3 \cosh{\left(x \right)}}{x^{2}} + \frac{2 \sinh{\left(x \right)}}{x^{3}}\right)
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