Производная 1/(atan(x))

Вы ввели

   1   
-------
atan(x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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