Производная atan(3*x)^4

Вы ввели

    4     
atan (3*x)

$$\operatorname{atan}^{4}{\left (3 x \right )}$$

Первая производная

       3     
12*atan (3*x)
-------------
          2  
   1 + 9*x   

$$\frac{12 \operatorname{atan}^{3}{\left (3 x \right )}}{9 x^{2} + 1}$$

Вторая производная

        2                         
108*atan (3*x)*(1 - 2*x*atan(3*x))
----------------------------------
                     2            
           /       2\             
           \1 + 9*x /             

$$\frac{108 \operatorname{atan}^{2}{\left (3 x \right )}}{\left(9 x^{2} + 1\right)^{2}} \left(- 2 x \operatorname{atan}{\left (3 x \right )} + 1\right)$$

Третья производная

    /                                               2     2     \          
    |      2           3       27*x*atan(3*x)   36*x *atan (3*x)|          
216*|- atan (3*x) + -------- - -------------- + ----------------|*atan(3*x)
    |                      2             2                 2    |          
    \               1 + 9*x       1 + 9*x           1 + 9*x     /          
---------------------------------------------------------------------------
                                          2                                
                                /       2\                                 
                                \1 + 9*x /                                 

$$\frac{216 \operatorname{atan}{\left (3 x \right )}}{\left(9 x^{2} + 1\right)^{2}} \left(\frac{36 x^{2} \operatorname{atan}^{2}{\left (3 x \right )}}{9 x^{2} + 1} - \frac{27 x \operatorname{atan}{\left (3 x \right )}}{9 x^{2} + 1} - \operatorname{atan}^{2}{\left (3 x \right )} + \frac{3}{9 x^{2} + 1}\right)$$