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