Derivada de (x^(e^tgx))

Ha introducido [src]

 / tan(x)\
 \E      /
x

x^{e^{\tan{\left(x \right)}}}

x^(E^tan(x))

Solución detallada

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

Perola derivada

$\left(\log{\left(e^{\tan{\left(x \right)}} \right)} + 1\right) e^{e^{\tan{\left(x \right)}} \tan{\left(x \right)}}$
Simplificamos:

$\left(\tan{\left(x \right)} + 1\right) e^{e^{\tan{\left(x \right)}} \tan{\left(x \right)}}$

Respuesta:

$\left(\tan{\left(x \right)} + 1\right) e^{e^{\tan{\left(x \right)}} \tan{\left(x \right)}}$

Primera derivada [src]

 / tan(x)\ / tan(x)                               \
 \E      / |e         /       2   \  tan(x)       |
x         *|------- + \1 + tan (x)/*e      *log(x)|
           \   x                                  /

x^{e^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) e^{\tan{\left(x \right)}} \log{\left(x \right)} + \frac{e^{\tan{\left(x \right)}}}{x}\right)

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Segunda derivada [src]

 / tan(x)\ /                    2                                    2             /       2   \                                \        
 \e      / |  1    /       2   \           /1   /       2   \       \   tan(x)   2*\1 + tan (x)/     /       2   \              |  tan(x)
x         *|- -- + \1 + tan (x)/ *log(x) + |- + \1 + tan (x)/*log(x)| *e       + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*e      
           |   2                           \x                       /                   x                                       |        
           \  x                                                                                                                 /

x^{e^{\tan{\left(x \right)}}} \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\tan{\left(x \right)}} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) e^{\tan{\left(x \right)}}

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Tercera derivada [src]

           /                                                                                                                                2                                                                                                                                                                                                                   \        
 / tan(x)\ |                  3                                    3               /       2   \                  2            /       2   \                                 /                    2            /       2   \                                \                                              /       2   \                         2              |        
 \e      / |2    /       2   \           /1   /       2   \       \   2*tan(x)   3*\1 + tan (x)/     /       2   \           3*\1 + tan (x)/      /1   /       2   \       \ |  1    /       2   \           2*\1 + tan (x)/     /       2   \              |  tan(x)        2    /       2   \          6*\1 + tan (x)/*tan(x)     /       2   \               |  tan(x)
x         *|-- + \1 + tan (x)/ *log(x) + |- + \1 + tan (x)/*log(x)| *e         - --------------- + 2*\1 + tan (x)/ *log(x) + ---------------- + 3*|- + \1 + tan (x)/*log(x)|*|- -- + \1 + tan (x)/ *log(x) + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*e       + 4*tan (x)*\1 + tan (x)/*log(x) + ---------------------- + 6*\1 + tan (x)/ *log(x)*tan(x)|*e      
           | 3                           \x                       /                      2                                          x             \x                       / |   2                                  x                                       |                                                      x                                            |        
           \x                                                                           x                                                                                    \  x                                                                           /                                                                                                   /

x^{e^{\tan{\left(x \right)}}} \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 \tan{\left(x \right)}} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) e^{\tan{\left(x \right)}} + \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + 6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} \tan{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2}{x^{3}}\right) e^{\tan{\left(x \right)}}

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Derivada de (x^(e^tgx))

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Definida a trozos:

Solución