Derivada de x^(tg(5x))

Ha introducido [src]

 tan(5*x)
x

$$x^{\tan{\left(5 x \right)}}$$

x^tan(5*x)

Solución detallada

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Perola derivada

$\left(\log{\left(\tan{\left(5 x \right)} \right)} + 1\right) \tan^{\tan{\left(5 x \right)}}{\left(5 x \right)}$

Respuesta:

$\left(\log{\left(\tan{\left(5 x \right)} \right)} + 1\right) \tan^{\tan{\left(5 x \right)}}{\left(5 x \right)}$

Gráfica

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Primera derivada [src]

 tan(5*x) /tan(5*x)   /         2     \       \
x        *|-------- + \5 + 5*tan (5*x)/*log(x)|
          \   x                               /

$$x^{\tan{\left(5 x \right)}} \left(\left(5 \tan^{2}{\left(5 x \right)} + 5\right) \log{\left(x \right)} + \frac{\tan{\left(5 x \right)}}{x}\right)$$

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Segunda derivada [src]

          /                                     2                 /       2     \                                     \
 tan(5*x) |/tan(5*x)     /       2     \       \    tan(5*x)   10*\1 + tan (5*x)/      /       2     \                |
x        *||-------- + 5*\1 + tan (5*x)/*log(x)|  - -------- + ------------------ + 50*\1 + tan (5*x)/*log(x)*tan(5*x)|
          |\   x                               /        2              x                                              |
          \                                            x                                                              /

$$x^{\tan{\left(5 x \right)}} \left(\left(5 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(5 x \right)}}{x}\right)^{2} + 50 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(x \right)} \tan{\left(5 x \right)} + \frac{10 \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x} - \frac{\tan{\left(5 x \right)}}{x^{2}}\right)$$

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Tercera derivada [src]

          /                                     3      /       2     \                                                        /                /       2     \                                     \                      2              /       2     \                                                \
 tan(5*x) |/tan(5*x)     /       2     \       \    15*\1 + tan (5*x)/   2*tan(5*x)     /tan(5*x)     /       2     \       \ |  tan(5*x)   10*\1 + tan (5*x)/      /       2     \                |       /       2     \           150*\1 + tan (5*x)/*tan(5*x)          2      /       2     \       |
x        *||-------- + 5*\1 + tan (5*x)/*log(x)|  - ------------------ + ---------- + 3*|-------- + 5*\1 + tan (5*x)/*log(x)|*|- -------- + ------------------ + 50*\1 + tan (5*x)/*log(x)*tan(5*x)| + 250*\1 + tan (5*x)/ *log(x) + ---------------------------- + 500*tan (5*x)*\1 + tan (5*x)/*log(x)|
          |\   x                               /             2                3         \   x                               / |      2              x                                              |                                              x                                                     |
          \                                                 x                x                                                \     x                                                              /                                                                                                    /

$$x^{\tan{\left(5 x \right)}} \left(\left(5 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(5 x \right)}}{x}\right)^{3} + 3 \left(5 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(5 x \right)}}{x}\right) \left(50 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(x \right)} \tan{\left(5 x \right)} + \frac{10 \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x} - \frac{\tan{\left(5 x \right)}}{x^{2}}\right) + 250 \left(\tan^{2}{\left(5 x \right)} + 1\right)^{2} \log{\left(x \right)} + 500 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(5 x \right)} + \frac{150 \left(\tan^{2}{\left(5 x \right)} + 1\right) \tan{\left(5 x \right)}}{x} - \frac{15 \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(5 x \right)}}{x^{3}}\right)$$

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Gráfico

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Expresiones idénticas

Derivada de x^(tg(5x))

Gráfico:

Definida a trozos:

Solución