Производная atan(3*x)^(5)

Вы ввели

    5     
atan (3*x)

$$\operatorname{atan}^{5}{\left (3 x \right )}$$

Первая производная

       4     
15*atan (3*x)
-------------
          2  
   1 + 9*x   

$$\frac{15 \operatorname{atan}^{4}{\left (3 x \right )}}{9 x^{2} + 1}$$

Вторая производная

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

$$\frac{90 \operatorname{atan}^{3}{\left (3 x \right )}}{\left(9 x^{2} + 1\right)^{2}} \left(- 3 x \operatorname{atan}{\left (3 x \right )} + 2\right)$$

Третья производная

               /                                               2     2     \
        2      |      2           6       36*x*atan(3*x)   36*x *atan (3*x)|
270*atan (3*x)*|- atan (3*x) + -------- - -------------- + ----------------|
               |                      2             2                 2    |
               \               1 + 9*x       1 + 9*x           1 + 9*x     /
----------------------------------------------------------------------------
                                          2                                 
                                /       2\                                  
                                \1 + 9*x /                                  

$$\frac{270 \operatorname{atan}^{2}{\left (3 x \right )}}{\left(9 x^{2} + 1\right)^{2}} \left(\frac{36 x^{2} \operatorname{atan}^{2}{\left (3 x \right )}}{9 x^{2} + 1} - \frac{36 x \operatorname{atan}{\left (3 x \right )}}{9 x^{2} + 1} - \operatorname{atan}^{2}{\left (3 x \right )} + \frac{6}{9 x^{2} + 1}\right)$$