Производная atan(x)^(32)

Вы ввели

    32   
atan  (x)

$$\operatorname{atan}^{32}{\left (x \right )}$$

Первая производная

       31   
32*atan  (x)
------------
        2   
   1 + x    

$$\frac{32 \operatorname{atan}^{31}{\left (x \right )}}{x^{2} + 1}$$

Вторая производная

       30                      
32*atan  (x)*(31 - 2*x*atan(x))
-------------------------------
                   2           
           /     2\            
           \1 + x /            

$$\frac{32 \operatorname{atan}^{30}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(- 2 x \operatorname{atan}{\left (x \right )} + 31\right)$$

Третья производная

             /                                        2     2   \
       29    |      2       465     93*x*atan(x)   4*x *atan (x)|
64*atan  (x)*|- atan (x) + ------ - ------------ + -------------|
             |                  2           2               2   |
             \             1 + x       1 + x           1 + x    /
-----------------------------------------------------------------
                                    2                            
                            /     2\                             
                            \1 + x /                             

$$\frac{64 \operatorname{atan}^{29}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left (x \right )}}{x^{2} + 1} - \frac{93 x \operatorname{atan}{\left (x \right )}}{x^{2} + 1} - \operatorname{atan}^{2}{\left (x \right )} + \frac{465}{x^{2} + 1}\right)$$