Derivada de y=x^tan(4x)

Ha introducido [src]

 tan(4*x)
x

x^{\tan{\left(4 x \right)}}

x^tan(4*x)

Solución detallada

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Perola derivada

$\left(\log{\left(\tan{\left(4 x \right)} \right)} + 1\right) \tan^{\tan{\left(4 x \right)}}{\left(4 x \right)}$

Respuesta:

$\left(\log{\left(\tan{\left(4 x \right)} \right)} + 1\right) \tan^{\tan{\left(4 x \right)}}{\left(4 x \right)}$

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

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

x^{\tan{\left(4 x \right)}} \left(\left(4 \tan^{2}{\left(4 x \right)} + 4\right) \log{\left(x \right)} + \frac{\tan{\left(4 x \right)}}{x}\right)

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Segunda derivada [src]

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

x^{\tan{\left(4 x \right)}} \left(\left(4 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(4 x \right)}}{x}\right)^{2} + 32 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(x \right)} \tan{\left(4 x \right)} + \frac{8 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x} - \frac{\tan{\left(4 x \right)}}{x^{2}}\right)

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Tercera derivada [src]

          /                                     3      /       2     \                                                        /               /       2     \                                     \                      2             /       2     \                                                \
 tan(4*x) |/tan(4*x)     /       2     \       \    12*\1 + tan (4*x)/   2*tan(4*x)     /tan(4*x)     /       2     \       \ |  tan(4*x)   8*\1 + tan (4*x)/      /       2     \                |       /       2     \           96*\1 + tan (4*x)/*tan(4*x)          2      /       2     \       |
x        *||-------- + 4*\1 + tan (4*x)/*log(x)|  - ------------------ + ---------- + 3*|-------- + 4*\1 + tan (4*x)/*log(x)|*|- -------- + ----------------- + 32*\1 + tan (4*x)/*log(x)*tan(4*x)| + 128*\1 + tan (4*x)/ *log(x) + --------------------------- + 256*tan (4*x)*\1 + tan (4*x)/*log(x)|
          |\   x                               /             2                3         \   x                               / |      2              x                                             |                                              x                                                    |
          \                                                 x                x                                                \     x                                                             /                                                                                                   /

x^{\tan{\left(4 x \right)}} \left(\left(4 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(4 x \right)}}{x}\right)^{3} + 3 \left(4 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(4 x \right)}}{x}\right) \left(32 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(x \right)} \tan{\left(4 x \right)} + \frac{8 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x} - \frac{\tan{\left(4 x \right)}}{x^{2}}\right) + 128 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} \log{\left(x \right)} + 256 \left(\tan^{2}{\left(4 x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(4 x \right)} + \frac{96 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)}}{x} - \frac{12 \left(\tan^{2}{\left(4 x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(4 x \right)}}{x^{3}}\right)

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Gráfico

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Derivada de y=x^tan(4x)

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