Производная log(asin(x))

Вы ввели

log(asin(x))

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

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

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