Derivada de y=x^tgx

Ha introducido [src]

 tan(x)
x

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

x^tan(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

 tan(x) /tan(x)   /       2   \       \
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   \       \    3*\1 + tan (x)/   2*tan(x)     /       2   \             /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |        2    /       2   \          6*\1 + tan (x)/*tan(x)|
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                          /            2             3                                  \  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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Expresiones idénticas

Derivada de y=x^tgx

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Solución