Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
log(x) /log(x*x + 1) 2*x*log(x)\
(x*x + 1) *|------------ + ----------|
\ x x*x + 1 /
$$\left(x x + 1\right)^{\log{\left(x \right)}} \left(\frac{2 x \log{\left(x \right)}}{x x + 1} + \frac{\log{\left(x x + 1 \right)}}{x}\right)$$
/ 2 \
log(x) |/ / 2\ \ / 2\ 2 |
/ 2\ ||log\1 + x / 2*x*log(x)| 4 log\1 + x / 2*log(x) 4*x *log(x)|
\1 + x / *||----------- + ----------| + ------ - ----------- + -------- - -----------|
|| x 2 | 2 2 2 2 |
|\ 1 + x / 1 + x x 1 + x / 2\ |
\ \1 + x / /
$$\left(x^{2} + 1\right)^{\log{\left(x \right)}} \left(- \frac{4 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x}\right)^{2} + \frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{4}{x^{2} + 1} - \frac{\log{\left(x^{2} + 1 \right)}}{x^{2}}\right)$$
/ 3 \
log(x) |/ / 2\ \ / / 2\ \ / / 2\ 2 \ / 2\ 3 |
/ 2\ ||log\1 + x / 2*x*log(x)| 12*x |log\1 + x / 2*x*log(x)| | 4 log\1 + x / 2*log(x) 4*x *log(x)| 2*log\1 + x / 12*x*log(x) 16*x *log(x)|
\1 + x / *||----------- + ----------| - --------- - 3*|----------- + ----------|*|- ------ + ----------- - -------- + -----------| + ------------- - ----------- + ------------|
|| x 2 | 2 | x 2 | | 2 2 2 2 | 3 2 3 |
|\ 1 + x / / 2\ \ 1 + x / | 1 + x x 1 + x / 2\ | x / 2\ / 2\ |
\ \1 + x / \ \1 + x / / \1 + x / \1 + x / /
$$\left(x^{2} + 1\right)^{\log{\left(x \right)}} \left(\frac{16 x^{3} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{12 x}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x}\right)^{3} - 3 \left(\frac{2 x \log{\left(x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x}\right) \left(\frac{4 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}}{x^{2} + 1} - \frac{4}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{x^{2}}\right) + \frac{2 \log{\left(x^{2} + 1 \right)}}{x^{3}}\right)$$