Производная atan(x)/x^3

Вы ввели

atan(x)
-------
    3  
   x   

$$\frac{1}{x^{3}} \operatorname{atan}{\left (x \right )}$$

Первая производная

     1        3*atan(x)
----------- - ---------
 3 /     2\        4   
x *\1 + x /       x    

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

Вторая производная

  /      1            3        6*atan(x)\
2*|- --------- - ----------- + ---------|
  |          2    2 /     2\        3   |
  |  /     2\    x *\1 + x /       x    |
  \  \1 + x /                           /
-----------------------------------------
                     2                   
                    x                    

$$\frac{1}{x^{2}} \left(- \frac{2}{\left(x^{2} + 1\right)^{2}} - \frac{6}{x^{2} \left(x^{2} + 1\right)} + \frac{12}{x^{3}} \operatorname{atan}{\left (x \right )}\right)$$

Третья производная

  /    2       15*atan(x)        4              9     \
4*|--------- - ---------- + ------------ + -----------|
  |        3        5                  2    4 /     2\|
  |/     2\        x         2 /     2\    x *\1 + x /|
  \\1 + x /                 x *\1 + x /               /
-------------------------------------------------------
                           x                           

$$\frac{1}{x} \left(\frac{8}{\left(x^{2} + 1\right)^{3}} + \frac{16}{x^{2} \left(x^{2} + 1\right)^{2}} + \frac{36}{x^{4} \left(x^{2} + 1\right)} - \frac{60}{x^{5}} \operatorname{atan}{\left (x \right )}\right)$$