Derivada de x^-tan(x)

Ha introducido [src]

 -tan(x)
x

$$x^{- \tan{\left(x \right)}}$$

x^(-tan(x))

Solución detallada

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Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

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

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

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Tercera derivada [src]

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

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

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Gráfico

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Derivada de x^-tan(x)

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