Производная (atan(9*x))^4

Вы ввели

    4     
atan (9*x)

$$\operatorname{atan}^{4}{\left (9 x \right )}$$

Первая производная

       3     
36*atan (9*x)
-------------
          2  
  1 + 81*x   

$$\frac{36 \operatorname{atan}^{3}{\left (9 x \right )}}{81 x^{2} + 1}$$

Вторая производная

        2                         
972*atan (9*x)*(1 - 6*x*atan(9*x))
----------------------------------
                      2           
           /        2\            
           \1 + 81*x /            

$$\frac{972 \operatorname{atan}^{2}{\left (9 x \right )}}{\left(81 x^{2} + 1\right)^{2}} \left(- 6 x \operatorname{atan}{\left (9 x \right )} + 1\right)$$

Третья производная

     /                                                 2     2     \          
     |      2            3       81*x*atan(9*x)   324*x *atan (9*x)|          
5832*|- atan (9*x) + --------- - -------------- + -----------------|*atan(9*x)
     |                       2             2                  2    |          
     \               1 + 81*x      1 + 81*x           1 + 81*x     /          
------------------------------------------------------------------------------
                                            2                                 
                                 /        2\                                  
                                 \1 + 81*x /                                  

$$\frac{5832 \operatorname{atan}{\left (9 x \right )}}{\left(81 x^{2} + 1\right)^{2}} \left(\frac{324 x^{2} \operatorname{atan}^{2}{\left (9 x \right )}}{81 x^{2} + 1} - \frac{81 x \operatorname{atan}{\left (9 x \right )}}{81 x^{2} + 1} - \operatorname{atan}^{2}{\left (9 x \right )} + \frac{3}{81 x^{2} + 1}\right)$$