Производная asin(2*x)^(5)

Вы ввели

    5     
asin (2*x)

$$\operatorname{asin}^{5}{\left (2 x \right )}$$

Первая производная

       4     
10*asin (2*x)
-------------
   __________
  /        2 
\/  1 - 4*x  

$$\frac{10 \operatorname{asin}^{4}{\left (2 x \right )}}{\sqrt{- 4 x^{2} + 1}}$$

Вторая производная

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

$$40 \left(\frac{x \operatorname{asin}{\left (2 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{2}{4 x^{2} - 1}\right) \operatorname{asin}^{3}{\left (2 x \right )}$$

Третья производная

              /                      2             2     2                      \
       2      |      12          asin (2*x)    12*x *asin (2*x)   24*x*asin(2*x)|
40*asin (2*x)*|------------- + ------------- + ---------------- + --------------|
              |          3/2             3/2              5/2                 2 |
              |/       2\      /       2\       /       2\         /        2\  |
              \\1 - 4*x /      \1 - 4*x /       \1 - 4*x /         \-1 + 4*x /  /

$$40 \left(\frac{12 x^{2} \operatorname{asin}^{2}{\left (2 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{24 x \operatorname{asin}{\left (2 x \right )}}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (2 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{12}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}^{2}{\left (2 x \right )}$$