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Derivada de y=x^(tg^2)x

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src]
    2     
 tan (x)  
x       *x
$$x x^{\tan^{2}{\left(x \right)}}$$
x^(tan(x)^2)*x
Solución detallada
  1. Se aplica la regla de la derivada de una multiplicación:

    ; calculamos :

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

      Perola derivada

    ; calculamos :

    1. Según el principio, aplicamos: tenemos

    Como resultado de:


Respuesta:

Primera derivada [src]
    2            2    /   2                                   \
 tan (x)      tan (x) |tan (x)   /         2   \              |
x        + x*x       *|------- + \2 + 2*tan (x)/*log(x)*tan(x)|
                      \   x                                   /
$$x x^{\tan^{2}{\left(x \right)}} \left(\left(2 \tan^{2}{\left(x \right)} + 2\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{\tan^{2}{\left(x \right)}}{x}\right) + x^{\tan^{2}{\left(x \right)}}$$
Segunda derivada [src]
    2    /  /                                 2              2                     2            /       2   \                                        \                                             \
 tan (x) |  |/tan(x)     /       2   \       \     2      tan (x)     /       2   \           4*\1 + tan (x)/*tan(x)        2    /       2   \       |     /tan(x)     /       2   \       \       |
x       *|x*||------ + 2*\1 + tan (x)/*log(x)| *tan (x) - ------- + 2*\1 + tan (x)/ *log(x) + ---------------------- + 4*tan (x)*\1 + tan (x)/*log(x)| + 2*|------ + 2*\1 + tan (x)/*log(x)|*tan(x)|
         |  |\  x                            /                2                                         x                                            |     \  x                            /       |
         \  \                                                x                                                                                       /                                             /
$$x^{\tan^{2}{\left(x \right)}} \left(x \left(\left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} \tan^{2}{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{\tan^{2}{\left(x \right)}}{x^{2}}\right) + 2 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \tan{\left(x \right)}\right)$$
Tercera derivada [src]
         /  /                                                                        2                                                                                                                                                                                                                                                                    \                                                                                                                                                 \
    2    |  |                                 3                2        /       2   \      /       2   \                                              /     2                     2            /       2   \                                        \                                                 2    /       2   \                   2              |        2                                         2                          2             /       2   \                                         |
 tan (x) |  |/tan(x)     /       2   \       \     3      2*tan (x)   6*\1 + tan (x)/    6*\1 + tan (x)/*tan(x)     /tan(x)     /       2   \       \ |  tan (x)     /       2   \           4*\1 + tan (x)/*tan(x)        2    /       2   \       |               3    /       2   \          12*tan (x)*\1 + tan (x)/      /       2   \               |   3*tan (x)     /tan(x)     /       2   \       \     2        /       2   \           12*\1 + tan (x)/*tan(x)         2    /       2   \       |
x       *|x*||------ + 2*\1 + tan (x)/*log(x)| *tan (x) + --------- + ---------------- - ---------------------- + 3*|------ + 2*\1 + tan (x)/*log(x)|*|- ------- + 2*\1 + tan (x)/ *log(x) + ---------------------- + 4*tan (x)*\1 + tan (x)/*log(x)|*tan(x) + 8*tan (x)*\1 + tan (x)/*log(x) + ------------------------ + 16*\1 + tan (x)/ *log(x)*tan(x)| - --------- + 3*|------ + 2*\1 + tan (x)/*log(x)| *tan (x) + 6*\1 + tan (x)/ *log(x) + ----------------------- + 12*tan (x)*\1 + tan (x)/*log(x)|
         |  |\  x                            /                 3             x                      2               \  x                            / |      2                                         x                                            |                                                      x                                              |        2        \  x                            /                                                 x                                             |
         \  \                                                 x                                    x                                                  \     x                                                                                       /                                                                                                     /       x                                                                                                                                         /
$$x^{\tan^{2}{\left(x \right)}} \left(x \left(\left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} \tan^{3}{\left(x \right)} + 3 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{\tan^{2}{\left(x \right)}}{x^{2}}\right) \tan{\left(x \right)} + 16 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} \tan{\left(x \right)} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{3}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x} + \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{x} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2}} + \frac{2 \tan^{2}{\left(x \right)}}{x^{3}}\right) + 3 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} \tan^{2}{\left(x \right)} + 6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 12 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \tan^{2}{\left(x \right)}}{x^{2}}\right)$$