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Derivada de x^exp(x*ln(x))

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Solución

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

    Perola derivada


Respuesta:

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