Производная log(1/asin(x))

Вы ввели

   /   1   \
log|-------|
   \asin(x)/

$$\log{\left (\frac{1}{\operatorname{asin}{\left (x \right )}} \right )}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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