Производная (asin(9*x))^4

Вы ввели

    4     
asin (9*x)

$$\operatorname{asin}^{4}{\left (9 x \right )}$$

Первая производная

       3      
36*asin (9*x) 
--------------
   ___________
  /         2 
\/  1 - 81*x  

$$\frac{36 \operatorname{asin}^{3}{\left (9 x \right )}}{\sqrt{- 81 x^{2} + 1}}$$

Вторая производная

        2      /      1        3*x*asin(9*x) \
972*asin (9*x)*|- ---------- + --------------|
               |           2              3/2|
               |  -1 + 81*x    /        2\   |
               \               \1 - 81*x /   /

$$972 \left(\frac{3 x \operatorname{asin}{\left (9 x \right )}}{\left(- 81 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{81 x^{2} - 1}\right) \operatorname{asin}^{2}{\left (9 x \right )}$$

Третья производная

     /                       2                                2     2     \          
     |      6            asin (9*x)     81*x*asin(9*x)   243*x *asin (9*x)|          
2916*|-------------- + -------------- + -------------- + -----------------|*asin(9*x)
     |           3/2              3/2               2                 5/2 |          
     |/        2\      /        2\      /         2\       /        2\    |          
     \\1 - 81*x /      \1 - 81*x /      \-1 + 81*x /       \1 - 81*x /    /          

$$2916 \left(\frac{243 x^{2} \operatorname{asin}^{2}{\left (9 x \right )}}{\left(- 81 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{81 x \operatorname{asin}{\left (9 x \right )}}{\left(81 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (9 x \right )}}{\left(- 81 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- 81 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}{\left (9 x \right )}$$