Производная atan(x)^(1/4)

Вы ввели

4 _________
\/ atan(x) 

$$\sqrt[4]{\operatorname{atan}{\left (x \right )}}$$

Первая производная

          1          
---------------------
  /     2\     3/4   
4*\1 + x /*atan   (x)

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

Вторая производная

    /   3         \    
   -|------- + 8*x|    
    \atan(x)      /    
-----------------------
           2           
   /     2\      3/4   
16*\1 + x / *atan   (x)

$$- \frac{8 x + \frac{3}{\operatorname{atan}{\left (x \right )}}}{16 \left(x^{2} + 1\right)^{2} \operatorname{atan}^{\frac{3}{4}}{\left (x \right )}}$$

Третья производная

          2                                             
  1    2*x              21                   9*x        
- - + ------ + -------------------- + ------------------
  2        2      /     2\     2        /     2\        
      1 + x    64*\1 + x /*atan (x)   8*\1 + x /*atan(x)
--------------------------------------------------------
                          2                             
                  /     2\      3/4                     
                  \1 + x / *atan   (x)                  

$$\frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{\frac{3}{4}}{\left (x \right )}} \left(\frac{2 x^{2}}{x^{2} + 1} + \frac{9 x}{8 \left(x^{2} + 1\right) \operatorname{atan}{\left (x \right )}} - \frac{1}{2} + \frac{21}{64 \left(x^{2} + 1\right) \operatorname{atan}^{2}{\left (x \right )}}\right)$$