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Derivada de y=(lnx)^x^3

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

Ha introducido [src]
        / 3\
        \x /
(log(x))    
$$\log{\left(x \right)}^{x^{3}}$$
log(x)^(x^3)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Primera derivada [src]
        / 3\ /   2                     \
        \x / |  x         2            |
(log(x))    *|------ + 3*x *log(log(x))|
             \log(x)                   /
$$\left(3 x^{2} \log{\left(\log{\left(x \right)} \right)} + \frac{x^{2}}{\log{\left(x \right)}}\right) \log{\left(x \right)}^{x^{3}}$$
Segunda derivada [src]
          / 3\ /                                                                2\
          \x / |     1        5                       3 /  1                   \ |
x*(log(x))    *|- ------- + ------ + 6*log(log(x)) + x *|------ + 3*log(log(x))| |
               |     2      log(x)                      \log(x)                / |
               \  log (x)                                                        /
$$x \left(x^{3} \left(3 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + 6 \log{\left(\log{\left(x \right)} \right)} + \frac{5}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{x^{3}}$$
Tercera derivada [src]
        / 3\ /                                                                          3                                                                     \
        \x / |     6         2                        11      6 /  1                   \       3 /  1                   \ /     1        5                   \|
(log(x))    *|- ------- + ------- + 6*log(log(x)) + ------ + x *|------ + 3*log(log(x))|  + 3*x *|------ + 3*log(log(x))|*|- ------- + ------ + 6*log(log(x))||
             |     2         3                      log(x)      \log(x)                /         \log(x)                / |     2      log(x)                ||
             \  log (x)   log (x)                                                                                         \  log (x)                         //
$$\left(x^{6} \left(3 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + 3 x^{3} \left(3 \log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \left(6 \log{\left(\log{\left(x \right)} \right)} + \frac{5}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) + 6 \log{\left(\log{\left(x \right)} \right)} + \frac{11}{\log{\left(x \right)}} - \frac{6}{\log{\left(x \right)}^{2}} + \frac{2}{\log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{x^{3}}$$