Производная atan(2*x)^3

Вы ввели

    3     
atan (2*x)

$$\operatorname{atan}^{3}{\left (2 x \right )}$$

Первая производная

      2     
6*atan (2*x)
------------
         2  
  1 + 4*x   

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

Вторая производная

24*(1 - 2*x*atan(2*x))*atan(2*x)
--------------------------------
                    2           
          /       2\            
          \1 + 4*x /            

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

Третья производная

   /                                             2     2     \
   |   1           2        12*x*atan(2*x)   16*x *atan (2*x)|
48*|-------- - atan (2*x) - -------------- + ----------------|
   |       2                          2                 2    |
   \1 + 4*x                    1 + 4*x           1 + 4*x     /
--------------------------------------------------------------
                                   2                          
                         /       2\                           
                         \1 + 4*x /                           

$$\frac{1}{\left(4 x^{2} + 1\right)^{2}} \left(\frac{768 x^{2} \operatorname{atan}^{2}{\left (2 x \right )}}{4 x^{2} + 1} - \frac{576 x \operatorname{atan}{\left (2 x \right )}}{4 x^{2} + 1} - 48 \operatorname{atan}^{2}{\left (2 x \right )} + \frac{48}{4 x^{2} + 1}\right)$$