Производная acot(7*x)^3

Вы ввели

    3     
acot (7*x)

$$\operatorname{acot}^{3}{\left (7 x \right )}$$

Первая производная

        2     
-21*acot (7*x)
--------------
          2   
  1 + 49*x    

$$- \frac{21 \operatorname{acot}^{2}{\left (7 x \right )}}{49 x^{2} + 1}$$

Вторая производная

294*(1 + 7*x*acot(7*x))*acot(7*x)
---------------------------------
                      2          
           /        2\           
           \1 + 49*x /           

$$\frac{294 \operatorname{acot}{\left (7 x \right )}}{\left(49 x^{2} + 1\right)^{2}} \left(7 x \operatorname{acot}{\left (7 x \right )} + 1\right)$$

Третья производная

     /                              2     2                      \
     |    2            1       196*x *acot (7*x)   42*x*acot(7*x)|
2058*|acot (7*x) - --------- - ----------------- - --------------|
     |                     2               2                 2   |
     \             1 + 49*x        1 + 49*x          1 + 49*x    /
------------------------------------------------------------------
                                      2                           
                           /        2\                            
                           \1 + 49*x /                            

$$\frac{1}{\left(49 x^{2} + 1\right)^{2}} \left(- \frac{403368 x^{2} \operatorname{acot}^{2}{\left (7 x \right )}}{49 x^{2} + 1} - \frac{86436 x \operatorname{acot}{\left (7 x \right )}}{49 x^{2} + 1} + 2058 \operatorname{acot}^{2}{\left (7 x \right )} - \frac{2058}{49 x^{2} + 1}\right)$$