Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ x*log(x)\ / x*log(x) \
\e / |e x*log(x) |
x *|--------- + (1 + log(x))*e *log(x)|
\ x /
$$x^{e^{x \log{\left(x \right)}}} \left(\left(\log{\left(x \right)} + 1\right) e^{x \log{\left(x \right)}} \log{\left(x \right)} + \frac{e^{x \log{\left(x \right)}}}{x}\right)$$
/ 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 /
$$x^{e^{x \log{\left(x \right)}}} \left(\left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} e^{x \log{\left(x \right)}} + \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) e^{x \log{\left(x \right)}}$$
/ 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 / /
$$x^{e^{x \log{\left(x \right)}}} \left(\left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 x \log{\left(x \right)}} + 3 \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) e^{x \log{\left(x \right)}} + \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)^{2}}{x} + \frac{3 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)}}{x} - \frac{3 \left(\log{\left(x \right)} + 1\right)}{x^{2}} - \frac{\log{\left(x \right)}}{x^{2}} + \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) e^{x \log{\left(x \right)}}$$