Производная (asin(7*x))^4

Вы ввели

    4     
asin (7*x)

$$\operatorname{asin}^{4}{\left (7 x \right )}$$

Первая производная

       3      
28*asin (7*x) 
--------------
   ___________
  /         2 
\/  1 - 49*x  

$$\frac{28 \operatorname{asin}^{3}{\left (7 x \right )}}{\sqrt{- 49 x^{2} + 1}}$$

Вторая производная

        2      /      3        7*x*asin(7*x) \
196*asin (7*x)*|- ---------- + --------------|
               |           2              3/2|
               |  -1 + 49*x    /        2\   |
               \               \1 - 49*x /   /

$$196 \left(\frac{7 x \operatorname{asin}{\left (7 x \right )}}{\left(- 49 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{49 x^{2} - 1}\right) \operatorname{asin}^{2}{\left (7 x \right )}$$

Третья производная

     /                       2                                2     2     \          
     |      6            asin (7*x)     63*x*asin(7*x)   147*x *asin (7*x)|          
1372*|-------------- + -------------- + -------------- + -----------------|*asin(7*x)
     |           3/2              3/2               2                 5/2 |          
     |/        2\      /        2\      /         2\       /        2\    |          
     \\1 - 49*x /      \1 - 49*x /      \-1 + 49*x /       \1 - 49*x /    /          

$$1372 \left(\frac{147 x^{2} \operatorname{asin}^{2}{\left (7 x \right )}}{\left(- 49 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{63 x \operatorname{asin}{\left (7 x \right )}}{\left(49 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (7 x \right )}}{\left(- 49 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- 49 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}{\left (7 x \right )}$$