Производная (acot(x))^4

Вы ввели

    4   
acot (x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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