Derivada de x^tg(2x)

Ha introducido [src]

 tan(2*x)
x

$$x^{\tan{\left(2 x \right)}}$$

x^tan(2*x)

Solución detallada

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Perola derivada

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

Respuesta:

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

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

          /                                     2                /       2     \                                    \
 tan(2*x) |/tan(2*x)     /       2     \       \    tan(2*x)   4*\1 + tan (2*x)/     /       2     \                |
x        *||-------- + 2*\1 + tan (2*x)/*log(x)|  - -------- + ----------------- + 8*\1 + tan (2*x)/*log(x)*tan(2*x)|
          |\   x                               /        2              x                                            |
          \                                            x                                                            /

$$x^{\tan{\left(2 x \right)}} \left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(2 x \right)}}{x}\right)^{2} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} \tan{\left(2 x \right)} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x} - \frac{\tan{\left(2 x \right)}}{x^{2}}\right)$$

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Tercera derivada [src]

          /                                     3     /       2     \                                                        /               /       2     \                                    \                     2             /       2     \                                               \
 tan(2*x) |/tan(2*x)     /       2     \       \    6*\1 + tan (2*x)/   2*tan(2*x)     /tan(2*x)     /       2     \       \ |  tan(2*x)   4*\1 + tan (2*x)/     /       2     \                |      /       2     \           24*\1 + tan (2*x)/*tan(2*x)         2      /       2     \       |
x        *||-------- + 2*\1 + tan (2*x)/*log(x)|  - ----------------- + ---------- + 3*|-------- + 2*\1 + tan (2*x)/*log(x)|*|- -------- + ----------------- + 8*\1 + tan (2*x)/*log(x)*tan(2*x)| + 16*\1 + tan (2*x)/ *log(x) + --------------------------- + 32*tan (2*x)*\1 + tan (2*x)/*log(x)|
          |\   x                               /             2               3         \   x                               / |      2              x                                            |                                             x                                                   |
          \                                                 x               x                                                \     x                                                            /                                                                                                 /

$$x^{\tan{\left(2 x \right)}} \left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(2 x \right)}}{x}\right)^{3} + 3 \left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(2 x \right)}}{x}\right) \left(8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} \tan{\left(2 x \right)} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x} - \frac{\tan{\left(2 x \right)}}{x^{2}}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(2 x \right)} + \frac{24 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x} - \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(2 x \right)}}{x^{3}}\right)$$

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Gráfico

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Derivada de x^tg(2x)

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