Derivada de y=(tanhx)^lnx

Ha introducido [src]

    log(x)   
tanh      (x)

\tanh^{\log{\left(x \right)}}{\left(x \right)}

tanh(x)^log(x)

Solución detallada

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Perola derivada

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

Respuesta:

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

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

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

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

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Tercera derivada [src]

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

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

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Gráfico

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Derivada de y=(tanhx)^lnx

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