Производная asin(1-x)^(3)

Вы ввели

    3       
asin (1 - x)

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

Первая производная

        2        
 -3*asin (1 - x) 
-----------------
   ______________
  /            2 
\/  1 - (1 - x)  

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

Вторая производная

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

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

Третья производная

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

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