Производная log(asin(x)^4)

Вы ввели

   /    4   \
log\asin (x)/

$$\log{\left (\operatorname{asin}^{4}{\left (x \right )} \right )}$$

Первая производная

         4         
-------------------
   ________        
  /      2         
\/  1 - x  *asin(x)

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

Вторая производная

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

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

Третья производная

  /                                            2                        \
  |     1                 2                 3*x              3*x        |
4*|----------- + -------------------- + ----------- - ------------------|
  |        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)                                 

$$\frac{1}{\operatorname{asin}{\left (x \right )}} \left(\frac{12 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{12 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} + \frac{4}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{8}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}}\right)$$