Производная 1/acos(x)^(2)

Вы ввели

   1    
--------
    2   
acos (x)

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

Первая производная

             2              
----------------------------
   ________                 
  /      2              2   
\/  1 - x  *acos(x)*acos (x)

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

Вторая производная

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

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

Третья производная

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

$$\frac{1}{\operatorname{acos}^{3}{\left (x \right )}} \left(\frac{6 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{18 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}{\left (x \right )}} + \frac{2}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{24}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left (x \right )}}\right)$$