Производная acot(x)^6

Вы ввели

    6   
acot (x)

$$\operatorname{acot}^{6}{\left (x \right )}$$

Первая производная

       5   
-6*acot (x)
-----------
        2  
   1 + x   

$$- \frac{6 \operatorname{acot}^{5}{\left (x \right )}}{x^{2} + 1}$$

Вторая производная

      4                     
6*acot (x)*(5 + 2*x*acot(x))
----------------------------
                 2          
         /     2\           
         \1 + x /           

$$\frac{6 \operatorname{acot}^{4}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(2 x \operatorname{acot}{\left (x \right )} + 5\right)$$

Третья производная

            /                                      2     2   \
       3    |    2        10     15*x*acot(x)   4*x *acot (x)|
12*acot (x)*|acot (x) - ------ - ------------ - -------------|
            |                2           2               2   |
            \           1 + x       1 + x           1 + x    /
--------------------------------------------------------------
                                  2                           
                          /     2\                            
                          \1 + x /                            

$$\frac{12 \operatorname{acot}^{3}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(- \frac{4 x^{2} \operatorname{acot}^{2}{\left (x \right )}}{x^{2} + 1} - \frac{15 x \operatorname{acot}{\left (x \right )}}{x^{2} + 1} + \operatorname{acot}^{2}{\left (x \right )} - \frac{10}{x^{2} + 1}\right)$$