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