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