Производная asin(3*x)^5

Вы ввели

    5     
asin (3*x)

$$\operatorname{asin}^{5}{\left (3 x \right )}$$

Первая производная

       4     
15*asin (3*x)
-------------
   __________
  /        2 
\/  1 - 9*x  

$$\frac{15 \operatorname{asin}^{4}{\left (3 x \right )}}{\sqrt{- 9 x^{2} + 1}}$$

Вторая производная

       3      /      4       3*x*asin(3*x)\
45*asin (3*x)*|- --------- + -------------|
              |          2             3/2|
              |  -1 + 9*x    /       2\   |
              \              \1 - 9*x /   /

$$45 \left(\frac{3 x \operatorname{asin}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{4}{9 x^{2} - 1}\right) \operatorname{asin}^{3}{\left (3 x \right )}$$

Третья производная

               /                      2             2     2                      \
        2      |      12          asin (3*x)    27*x *asin (3*x)   36*x*asin(3*x)|
135*asin (3*x)*|------------- + ------------- + ---------------- + --------------|
               |          3/2             3/2              5/2                 2 |
               |/       2\      /       2\       /       2\         /        2\  |
               \\1 - 9*x /      \1 - 9*x /       \1 - 9*x /         \-1 + 9*x /  /

$$135 \left(\frac{27 x^{2} \operatorname{asin}^{2}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{36 x \operatorname{asin}{\left (3 x \right )}}{\left(9 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{12}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}^{2}{\left (3 x \right )}$$