The first derivative
[src]
4
2*cos (x) 3
- -------------- - 4*cos (x)*acot(2*x - 3)*sin(x)
2
1 + (2*x - 3)
$$- 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)} \operatorname{acot}{\left(2 x - 3 \right)} - \frac{2 \cos^{4}{\left(x \right)}}{\left(2 x - 3\right)^{2} + 1}$$
The second derivative
[src]
/ 2 \
2 |/ 2 2 \ 2*cos (x)*(-3 + 2*x) 4*cos(x)*sin(x)|
4*cos (x)*|\- cos (x) + 3*sin (x)/*acot(-3 + 2*x) + -------------------- + ---------------|
| 2 2|
| / 2\ 1 + (-3 + 2*x) |
\ \1 + (-3 + 2*x) / /
$$4 \left(\frac{2 \left(2 x - 3\right) \cos^{2}{\left(x \right)}}{\left(\left(2 x - 3\right)^{2} + 1\right)^{2}} + \left(3 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{acot}{\left(2 x - 3 \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\left(2 x - 3\right)^{2} + 1}\right) \cos^{2}{\left(x \right)}$$
The third derivative
[src]
/ / 2 \ \
| 3 | 4*(-3 + 2*x) | |
| 2*cos (x)*|-1 + ---------------| |
| | 2| / 2 2 \ 2 |
|/ 2 2 \ \ 1 + (-3 + 2*x) / 3*\- cos (x) + 3*sin (x)/*cos(x) 12*cos (x)*(-3 + 2*x)*sin(x)|
-8*|\- 5*cos (x) + 3*sin (x)/*acot(-3 + 2*x)*sin(x) + -------------------------------- + -------------------------------- + ----------------------------|*cos(x)
| 2 2 2 |
| / 2\ 1 + (-3 + 2*x) / 2\ |
\ \1 + (-3 + 2*x) / \1 + (-3 + 2*x) / /
$$- 8 \left(\frac{12 \left(2 x - 3\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\left(2 x - 3\right)^{2} + 1\right)^{2}} + \frac{2 \left(\frac{4 \left(2 x - 3\right)^{2}}{\left(2 x - 3\right)^{2} + 1} - 1\right) \cos^{3}{\left(x \right)}}{\left(\left(2 x - 3\right)^{2} + 1\right)^{2}} + \left(3 \sin^{2}{\left(x \right)} - 5 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{acot}{\left(2 x - 3 \right)} + \frac{3 \left(3 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{\left(2 x - 3\right)^{2} + 1}\right) \cos{\left(x \right)}$$