Производная acot(x)^(1/4)

Вы ввели

4 _________
\/ acot(x) 

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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