Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
atan(x) /atan(x) log(x)\
x *|------- + ------|
| x 2|
\ 1 + x /
$$x^{\operatorname{atan}{\left(x \right)}} \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)$$
The second derivative
[src]
/ 2 \
atan(x) |/atan(x) log(x)\ atan(x) 2 2*x*log(x)|
x *||------- + ------| - ------- + ---------- - ----------|
|| x 2| 2 / 2\ 2 |
|\ 1 + x / x x*\1 + x / / 2\ |
\ \1 + x / /
$$x^{\operatorname{atan}{\left(x \right)}} \left(- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{2} + \frac{2}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2}}\right)$$
The third derivative
[src]
/ 3 2 \
atan(x) |/atan(x) log(x)\ 6 3 /atan(x) log(x)\ /atan(x) 2 2*x*log(x)\ 2*log(x) 2*atan(x) 8*x *log(x)|
x *||------- + ------| - --------- - ----------- - 3*|------- + ------|*|------- - ---------- + ----------| - --------- + --------- + -----------|
|| x 2| 2 2 / 2\ | x 2| | 2 / 2\ 2 | 2 3 3 |
|\ 1 + x / / 2\ x *\1 + x / \ 1 + x / | x x*\1 + x / / 2\ | / 2\ x / 2\ |
\ \1 + x / \ \1 + x / / \1 + x / \1 + x / /
$$x^{\operatorname{atan}{\left(x \right)}} \left(\frac{8 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{3} - 3 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right) \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{2}}\right) - \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(x^{2} + 1\right)^{2}} - \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}{\left(x \right)}}{x^{3}}\right)$$