Производная (atan(6*x))^3

Вы ввели

    3     
atan (6*x)

$$\operatorname{atan}^{3}{\left (6 x \right )}$$

Первая производная

       2     
18*atan (6*x)
-------------
          2  
  1 + 36*x   

$$\frac{18 \operatorname{atan}^{2}{\left (6 x \right )}}{36 x^{2} + 1}$$

Вторая производная

216*(1 - 6*x*atan(6*x))*atan(6*x)
---------------------------------
                      2          
           /        2\           
           \1 + 36*x /           

$$\frac{216 \operatorname{atan}{\left (6 x \right )}}{\left(36 x^{2} + 1\right)^{2}} \left(- 6 x \operatorname{atan}{\left (6 x \right )} + 1\right)$$

Третья производная

     /                                               2     2     \
     |    1           2        36*x*atan(6*x)   144*x *atan (6*x)|
1296*|--------- - atan (6*x) - -------------- + -----------------|
     |        2                          2                  2    |
     \1 + 36*x                   1 + 36*x           1 + 36*x     /
------------------------------------------------------------------
                                      2                           
                           /        2\                            
                           \1 + 36*x /                            

$$\frac{1}{\left(36 x^{2} + 1\right)^{2}} \left(\frac{186624 x^{2} \operatorname{atan}^{2}{\left (6 x \right )}}{36 x^{2} + 1} - \frac{46656 x \operatorname{atan}{\left (6 x \right )}}{36 x^{2} + 1} - 1296 \operatorname{atan}^{2}{\left (6 x \right )} + \frac{1296}{36 x^{2} + 1}\right)$$