Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ 2\
\x /
/log(x)\ / x /log(x)\\
|------| *|------ + 2*x*log|------||
\log(5)/ \log(x) \log(5)//
$$\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)^{x^{2}} \left(2 x \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{x}{\log{\left(x \right)}}\right)$$
/ 2\
\x / / 2\
/log(x)\ | 1 /log(x)\ 3 2 / 1 /log(x)\\ |
|------| *|- ------- + 2*log|------| + ------ + x *|------ + 2*log|------|| |
\log(5)/ | 2 \log(5)/ log(x) \log(x) \log(5)// |
\ log (x) /
$$\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)^{x^{2}} \left(x^{2} \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} + 2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{3}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right)$$
/ 3 2 \
/ 2\ | 2 - ------ + ------- |
\x / | 3 log(x) 2 |
/log(x)\ | 3 / 1 /log(x)\\ log (x) / 1 /log(x)\\ / 1 /log(x)\ 3 \|
|------| *|x *|------ + 2*log|------|| + -------------------- + 3*x*|------ + 2*log|------||*|- ------- + 2*log|------| + ------||
\log(5)/ | \log(x) \log(5)// x*log(x) \log(x) \log(5)// | 2 \log(5)/ log(x)||
\ \ log (x) //
$$\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)^{x^{2}} \left(x^{3} \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + 3 x \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{1}{\log{\left(x \right)}}\right) \left(2 \log{\left(\frac{\log{\left(x \right)}}{\log{\left(5 \right)}} \right)} + \frac{3}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}^{2}}\right) + \frac{2 - \frac{3}{\log{\left(x \right)}} + \frac{2}{\log{\left(x \right)}^{2}}}{x \log{\left(x \right)}}\right)$$