Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
acot(x) /acot(x) log(x)\
x *|------- - ------|
| x 2|
\ 1 + x /
$$x^{\operatorname{acot}{\left(x \right)}} \left(- \frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{acot}{\left(x \right)}}{x}\right)$$
/ 2 \
acot(x) |/log(x) acot(x)\ acot(x) 2 2*x*log(x)|
x *||------ - -------| - ------- - ---------- + ----------|
|| 2 x | 2 / 2\ 2 |
|\1 + x / x x*\1 + x / / 2\ |
\ \1 + x / /
$$x^{\operatorname{acot}{\left(x \right)}} \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{\log{\left(x \right)}}{x^{2} + 1} - \frac{\operatorname{acot}{\left(x \right)}}{x}\right)^{2} - \frac{2}{x \left(x^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x \right)}}{x^{2}}\right)$$
/ 3 2 \
acot(x) | /log(x) acot(x)\ 6 2*acot(x) 2*log(x) 3 /log(x) acot(x)\ /acot(x) 2 2*x*log(x)\ 8*x *log(x)|
x *|- |------ - -------| + --------- + --------- + --------- + ----------- + 3*|------ - -------|*|------- + ---------- - ----------| - -----------|
| | 2 x | 2 3 2 2 / 2\ | 2 x | | 2 / 2\ 2 | 3 |
| \1 + x / / 2\ x / 2\ x *\1 + x / \1 + x / | x x*\1 + x / / 2\ | / 2\ |
\ \1 + x / \1 + x / \ \1 + x / / \1 + x / /
$$x^{\operatorname{acot}{\left(x \right)}} \left(- \frac{8 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \left(\frac{\log{\left(x \right)}}{x^{2} + 1} - \frac{\operatorname{acot}{\left(x \right)}}{x}\right)^{3} + 3 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} - \frac{\operatorname{acot}{\left(x \right)}}{x}\right) \left(- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{x \left(x^{2} + 1\right)} + \frac{\operatorname{acot}{\left(x \right)}}{x^{2}}\right) + \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{\left(x^{2} + 1\right)^{2}} + \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x \right)}}{x^{3}}\right)$$