Производная atan(x)^(-2)

Вы ввели

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

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

Первая производная

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

$$- \frac{2}{\left(x^{2} + 1\right) \operatorname{atan}^{3}{\left (x \right )}}$$

Вторая производная

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

$$\frac{4 x + \frac{6}{\operatorname{atan}{\left (x \right )}}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{3}{\left (x \right )}}$$

Третья производная

  /                            2                    \
  |            6            4*x           9*x       |
4*|1 - ----------------- - ------ - ----------------|
  |    /     2\     2           2   /     2\        |
  \    \1 + x /*atan (x)   1 + x    \1 + x /*atan(x)/
-----------------------------------------------------
                          2                          
                  /     2\      3                    
                  \1 + x / *atan (x)                 

$$\frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{3}{\left (x \right )}} \left(- \frac{16 x^{2}}{x^{2} + 1} - \frac{36 x}{\left(x^{2} + 1\right) \operatorname{atan}{\left (x \right )}} + 4 - \frac{24}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left (x \right )}}\right)$$