Производная acot(5*x)^(3)

Вы ввели

    3     
acot (5*x)

$$\operatorname{acot}^{3}{\left (5 x \right )}$$

Первая производная

        2     
-15*acot (5*x)
--------------
          2   
  1 + 25*x    

$$- \frac{15 \operatorname{acot}^{2}{\left (5 x \right )}}{25 x^{2} + 1}$$

Вторая производная

150*(1 + 5*x*acot(5*x))*acot(5*x)
---------------------------------
                      2          
           /        2\           
           \1 + 25*x /           

$$\frac{150 \operatorname{acot}{\left (5 x \right )}}{\left(25 x^{2} + 1\right)^{2}} \left(5 x \operatorname{acot}{\left (5 x \right )} + 1\right)$$

Третья производная

    /                              2     2                      \
    |    2            1       100*x *acot (5*x)   30*x*acot(5*x)|
750*|acot (5*x) - --------- - ----------------- - --------------|
    |                     2               2                 2   |
    \             1 + 25*x        1 + 25*x          1 + 25*x    /
-----------------------------------------------------------------
                                      2                          
                           /        2\                           
                           \1 + 25*x /                           

$$\frac{1}{\left(25 x^{2} + 1\right)^{2}} \left(- \frac{75000 x^{2} \operatorname{acot}^{2}{\left (5 x \right )}}{25 x^{2} + 1} - \frac{22500 x \operatorname{acot}{\left (5 x \right )}}{25 x^{2} + 1} + 750 \operatorname{acot}^{2}{\left (5 x \right )} - \frac{750}{25 x^{2} + 1}\right)$$