Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
2 / 2 \
atan (x) |atan (x) 2*atan(x)*log(x)|
x *|-------- + ----------------|
| x 2 |
\ 1 + x /
$$x^{\operatorname{atan}^{2}{\left(x \right)}} \left(\frac{2 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x}\right)$$
2 / 2 2 \
atan (x) |/atan(x) 2*log(x)\ 2 atan (x) 2*log(x) 4*atan(x) 4*x*atan(x)*log(x)|
x *||------- + --------| *atan (x) - -------- + --------- + ---------- - ------------------|
|| x 2 | 2 2 / 2\ 2 |
|\ 1 + x / x / 2\ x*\1 + x / / 2\ |
\ \1 + x / \1 + x / /
$$x^{\operatorname{atan}^{2}{\left(x \right)}} \left(- \frac{4 x \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{2} \operatorname{atan}^{2}{\left(x \right)} + \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{4 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right)$$
2 / 3 2 / 2 \ 2 \
atan (x) |/atan(x) 2*log(x)\ 3 12*atan(x) 2*atan (x) 6 12*x*log(x) 6*atan(x) 4*atan(x)*log(x) /atan(x) 2*log(x)\ |atan (x) 2*log(x) 4*atan(x) 4*x*atan(x)*log(x)| 16*x *atan(x)*log(x)|
x *||------- + --------| *atan (x) - ---------- + ---------- + ----------- - ----------- - ----------- - ---------------- - 3*|------- + --------|*|-------- - --------- - ---------- + ------------------|*atan(x) + --------------------|
|| x 2 | 2 3 2 3 2 / 2\ 2 | x 2 | | 2 2 / 2\ 2 | 3 |
|\ 1 + x / / 2\ x / 2\ / 2\ x *\1 + x / / 2\ \ 1 + x / | x / 2\ x*\1 + x / / 2\ | / 2\ |
\ \1 + x / x*\1 + x / \1 + x / \1 + x / \ \1 + x / \1 + x / / \1 + x / /
$$x^{\operatorname{atan}^{2}{\left(x \right)}} \left(\frac{16 x^{2} \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \left(\frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{3} \operatorname{atan}^{3}{\left(x \right)} - 3 \left(\frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right) \left(\frac{4 x \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{4 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) \operatorname{atan}{\left(x \right)} - \frac{4 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{x \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}^{2}{\left(x \right)}}{x^{3}}\right)$$