Производная acot(x)/x^2

Вы ввели

acot(x)
-------
    2  
   x   

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

Первая производная

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

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

Вторая производная

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

$$\frac{1}{x} \left(\frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{4}{x^{2} \left(x^{2} + 1\right)} + \frac{6}{x^{3}} \operatorname{acot}{\left (x \right )}\right)$$

Третья производная

   /    4            5              9        12*acot(x)\
-2*|--------- + ------------ + ----------- + ----------|
   |        3              2    4 /     2\        5    |
   |/     2\     2 /     2\    x *\1 + x /       x     |
   \\1 + x /    x *\1 + x /                            /

$$- 2 \left(\frac{4}{\left(x^{2} + 1\right)^{3}} + \frac{5}{x^{2} \left(x^{2} + 1\right)^{2}} + \frac{9}{x^{4} \left(x^{2} + 1\right)} + \frac{12}{x^{5}} \operatorname{acot}{\left (x \right )}\right)$$