Производная 1/(atan(x)+2)

Вы ввели

     1     
-----------
atan(x) + 2

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

  /        2                                                    \
  |     4*x                3                       6*x          |
2*|1 - ------ - ----------------------- - ----------------------|
  |         2   /     2\              2   /     2\              |
  \    1 + x    \1 + x /*(2 + atan(x))    \1 + x /*(2 + atan(x))/
-----------------------------------------------------------------
                             2                                   
                     /     2\               2                    
                     \1 + x / *(2 + atan(x))                     

$$\frac{1}{\left(x^{2} + 1\right)^{2} \left(\operatorname{atan}{\left (x \right )} + 2\right)^{2}} \left(- \frac{8 x^{2}}{x^{2} + 1} - \frac{12 x}{\left(x^{2} + 1\right) \left(\operatorname{atan}{\left (x \right )} + 2\right)} + 2 - \frac{6}{\left(x^{2} + 1\right) \left(\operatorname{atan}{\left (x \right )} + 2\right)^{2}}\right)$$