Производная 5/asin(x)

Вы ввели

   5   
-------
asin(x)

$$\frac{5}{\operatorname{asin}{\left (x \right )}}$$

Первая производная

        -5          
--------------------
   ________         
  /      2      2   
\/  1 - x  *asin (x)

$$- \frac{5}{\sqrt{- x^{2} + 1} \operatorname{asin}^{2}{\left (x \right )}}$$

Вторая производная

   /     x                2        \
-5*|----------- + -----------------|
   |        3/2   /      2\        |
   |/     2\      \-1 + x /*asin(x)|
   \\1 - x /                       /
------------------------------------
                  2                 
              asin (x)              

$$- \frac{1}{\operatorname{asin}^{2}{\left (x \right )}} \left(\frac{5 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{10}{\left(x^{2} - 1\right) \operatorname{asin}{\left (x \right )}}\right)$$

Третья производная

  /                                              2                        \
  |       1                 6                 3*x              6*x        |
5*|- ----------- - -------------------- - ----------- + ------------------|
  |          3/2           3/2                    5/2            2        |
  |  /     2\      /     2\        2      /     2\      /      2\         |
  \  \1 - x /      \1 - x /   *asin (x)   \1 - x /      \-1 + x / *asin(x)/
---------------------------------------------------------------------------
                                      2                                    
                                  asin (x)                                 

$$\frac{1}{\operatorname{asin}^{2}{\left (x \right )}} \left(- \frac{15 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{30 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} - \frac{5}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{30}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}}\right)$$