Производная acot(2*x)^(3)

Вы ввели

    3     
acot (2*x)

$$\operatorname{acot}^{3}{\left (2 x \right )}$$

Первая производная

       2     
-6*acot (2*x)
-------------
          2  
   1 + 4*x   

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

Вторая производная

24*(1 + 2*x*acot(2*x))*acot(2*x)
--------------------------------
                    2           
          /       2\            
          \1 + 4*x /            

$$\frac{24 \operatorname{acot}{\left (2 x \right )}}{\left(4 x^{2} + 1\right)^{2}} \left(2 x \operatorname{acot}{\left (2 x \right )} + 1\right)$$

Третья производная

   /                            2     2                      \
   |    2           1       16*x *acot (2*x)   12*x*acot(2*x)|
48*|acot (2*x) - -------- - ---------------- - --------------|
   |                    2              2                 2   |
   \             1 + 4*x        1 + 4*x           1 + 4*x    /
--------------------------------------------------------------
                                   2                          
                         /       2\                           
                         \1 + 4*x /                           

$$\frac{1}{\left(4 x^{2} + 1\right)^{2}} \left(- \frac{768 x^{2} \operatorname{acot}^{2}{\left (2 x \right )}}{4 x^{2} + 1} - \frac{576 x \operatorname{acot}{\left (2 x \right )}}{4 x^{2} + 1} + 48 \operatorname{acot}^{2}{\left (2 x \right )} - \frac{48}{4 x^{2} + 1}\right)$$