The second derivative
[src]
/ 2 / 2 \ \
| x / x \ | 4*x | |
2*|1 - ------ - 2*x*|------ + atan(x)| + x*|-1 + ------|*atan(x)|
| 2 | 2 | | 2| |
\ 1 + x \1 + x / \ 1 + x / /
-----------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{2 \left(- \frac{x^{2}}{x^{2} + 1} - 2 x \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}$$
The third derivative
[src]
/ / 2 \ / 2 \ \
| | x | 2 | 2*x | |
| 10*x*|-1 + ------| 12*x *|-1 + ------|*atan(x)|
| / 2 \ | 2| | 2| |
| | 4*x | / x \ \ 1 + x / \ 1 + x / |
2*|3*|-1 + ------|*|------ + atan(x)| + ------------------ - ---------------------------|
| | 2| | 2 | 2 2 |
\ \ 1 + x / \1 + x / 1 + x 1 + x /
-----------------------------------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{2 \left(- \frac{12 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{10 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} + 3 \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)\right)}{\left(x^{2} + 1\right)^{2}}$$