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The derivative of the function/ arcctg(2x-3)*cos^4x

Derivative of arcctg(2x-3)*cos^4x

Function f() - derivative -N order at the point
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The solution

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                 4   
acot(2*x - 3)*cos (x)
cos⁡4(x)acot⁡(2x−3)\cos^{4}{\left(x \right)} \operatorname{acot}{\left(2 x - 3 \right)} 
acot(2*x - 3)*cos(x)^4
The graph
02468-8-6-4-2-10101.0-1.0
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
         4                                       
    2*cos (x)           3                        
- -------------- - 4*cos (x)*acot(2*x - 3)*sin(x)
               2                                 
  1 + (2*x - 3)
−4sin⁡(x)cos⁡3(x)acot⁡(2x−3)−2cos⁡4(x)(2x−3)2+1- 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}
Simplify
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(2(2x−3)cos⁡2(x)((2x−3)2+1)2+(3sin⁡2(x)−cos⁡2(x))acot⁡(2x−3)+4sin⁡(x)cos⁡(x)(2x−3)2+1)cos⁡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)}
Simplify
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(12(2x−3)sin⁡(x)cos⁡2(x)((2x−3)2+1)2+2(4(2x−3)2(2x−3)2+1−1)cos⁡3(x)((2x−3)2+1)2+(3sin⁡2(x)−5cos⁡2(x))sin⁡(x)acot⁡(2x−3)+3(3sin⁡2(x)−cos⁡2(x))cos⁡(x)(2x−3)2+1)cos⁡(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)}
Simplify
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