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Derivative of x*arctg(x)ctg(x)*cos(x)

Function f() - derivative -N order at the point
v

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x*atan(x)*cot(x)*cos(x)
$$x \operatorname{atan}{\left(x \right)} \cot{\left(x \right)} \cos{\left(x \right)}$$
((x*atan(x))*cot(x))*cos(x)
The graph
The first derivative [src]
//  x             \            /        2   \        \                                 
||------ + atan(x)|*cot(x) + x*\-1 - cot (x)/*atan(x)|*cos(x) - x*atan(x)*cot(x)*sin(x)
||     2          |                                  |                                 
\\1 + x           /                                  /                                 
$$- x \sin{\left(x \right)} \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + \left(x \left(- \cot^{2}{\left(x \right)} - 1\right) \operatorname{atan}{\left(x \right)} + \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \cot{\left(x \right)}\right) \cos{\left(x \right)}$$
The second derivative [src]
    /                                   /        2  \                                        \                                                                                                    
    |                                   |       x   |                                        |                                                                                                    
    |                                   |-1 + ------|*cot(x)                                 |                                                                                                    
    |                                   |          2|                                        |                                                                                                    
    |/       2   \ /  x             \   \     1 + x /            /       2   \               |            /  /  x             \            /       2   \        \                                 
- 2*|\1 + cot (x)/*|------ + atan(x)| + -------------------- - x*\1 + cot (x)/*atan(x)*cot(x)|*cos(x) + 2*|- |------ + atan(x)|*cot(x) + x*\1 + cot (x)/*atan(x)|*sin(x) - x*atan(x)*cos(x)*cot(x)
    |              |     2          |               2                                        |            |  |     2          |                                 |                                 
    \              \1 + x           /          1 + x                                         /            \  \1 + x           /                                 /                                 
$$- x \cos{\left(x \right)} \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + 2 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} - \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \cot{\left(x \right)}\right) \sin{\left(x \right)} - 2 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right) \cot{\left(x \right)}}{x^{2} + 1}\right) \cos{\left(x \right)}$$
The third derivative [src]
  /                /        2  \                                                                                             /        2  \       \                                                                               /                                   /        2  \                                        \                                 
  |  /       2   \ |       x   |                                                                                             |       x   |       |                                                                               |                                   |       x   |                                        |                                 
  |3*\1 + cot (x)/*|-1 + ------|                                                                                         4*x*|-1 + ------|*cot(x)|                                                                               |                                   |-1 + ------|*cot(x)                                 |                                 
  |                |          2|                                                                                             |          2|       |                                                                               |                                   |          2|                                        |                                 
  |                \     1 + x /     /       2   \ /  x             \            /       2   \ /         2   \               \     1 + x /       |            /  /  x             \            /       2   \        \            |/       2   \ /  x             \   \     1 + x /            /       2   \               |                                 
2*|----------------------------- + 3*\1 + cot (x)/*|------ + atan(x)|*cot(x) - x*\1 + cot (x)/*\1 + 3*cot (x)/*atan(x) + ------------------------|*cos(x) + 3*|- |------ + atan(x)|*cot(x) + x*\1 + cot (x)/*atan(x)|*cos(x) + 6*|\1 + cot (x)/*|------ + atan(x)| + -------------------- - x*\1 + cot (x)/*atan(x)*cot(x)|*sin(x) + x*atan(x)*cot(x)*sin(x)
  |                 2                              |     2          |                                                                   2        |            |  |     2          |                                 |            |              |     2          |               2                                        |                                 
  |            1 + x                               \1 + x           /                                                           /     2\         |            \  \1 + x           /                                 /            \              \1 + x           /          1 + x                                         /                                 
  \                                                                                                                             \1 + x /         /                                                                                                                                                                                                          
$$x \sin{\left(x \right)} \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + 3 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} - \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \cot{\left(x \right)}\right) \cos{\left(x \right)} + 6 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)} + \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right) \cot{\left(x \right)}}{x^{2} + 1}\right) \sin{\left(x \right)} + 2 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} + \frac{4 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right) \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + 3 \left(\frac{x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \frac{3 \left(\frac{x^{2}}{x^{2} + 1} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2} + 1}\right) \cos{\left(x \right)}$$