Производная acot(atan(x))

Вы ввели

acot(atan(x))

$$\operatorname{acot}{\left(\operatorname{atan}{\left(x \right)} \right)}$$

d                
--(acot(atan(x)))
dx               

$$\frac{d}{d x} \operatorname{acot}{\left(\operatorname{atan}{\left(x \right)} \right)}$$

Первая производная

          -1           
-----------------------
/     2\ /        2   \
\1 + x /*\1 + atan (x)/

$$- \frac{1}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)}$$

Вторая производная

    /      atan(x)   \  
  2*|x + ------------|  
    |            2   |  
    \    1 + atan (x)/  
------------------------
        2               
/     2\  /        2   \
\1 + x / *\1 + atan (x)/

$$\frac{2 \left(x + \frac{\operatorname{atan}{\left(x \right)}}{\operatorname{atan}^{2}{\left(x \right)} + 1}\right)}{\left(x^{2} + 1\right)^{2} \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)}$$

Третья производная

  /                                  2                 2                                    \
  |               1               4*x            4*atan (x)                6*x*atan(x)      |
2*|1 + ----------------------- - ------ - ------------------------ - -----------------------|
  |    /     2\ /        2   \        2                          2   /     2\ /        2   \|
  |    \1 + x /*\1 + atan (x)/   1 + x    /     2\ /        2   \    \1 + x /*\1 + atan (x)/|
  \                                       \1 + x /*\1 + atan (x)/                           /
---------------------------------------------------------------------------------------------
                                           2                                                 
                                   /     2\  /        2   \                                  
                                   \1 + x / *\1 + atan (x)/                                  

$$\frac{2 \left(- \frac{4 x^{2}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)} + 1 + \frac{1}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)} - \frac{4 \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)^{2}}\right)}{\left(x^{2} + 1\right)^{2} \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)}$$

График