Производная asin(3*x)^(4)

Вы ввели

    4     
asin (3*x)

$$\operatorname{asin}^{4}{\left (3 x \right )}$$

Первая производная

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

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

Вторая производная

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

$$108 \left(\frac{x \operatorname{asin}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{9 x^{2} - 1}\right) \operatorname{asin}^{2}{\left (3 x \right )}$$

Третья производная

    /                      2                              2     2     \          
    |      6           asin (3*x)    27*x*asin(3*x)   27*x *asin (3*x)|          
108*|------------- + ------------- + -------------- + ----------------|*asin(3*x)
    |          3/2             3/2               2               5/2  |          
    |/       2\      /       2\       /        2\      /       2\     |          
    \\1 - 9*x /      \1 - 9*x /       \-1 + 9*x /      \1 - 9*x /     /          

$$108 \left(\frac{27 x^{2} \operatorname{asin}^{2}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{27 x \operatorname{asin}{\left (3 x \right )}}{\left(9 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (3 x \right )}}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- 9 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}{\left (3 x \right )}$$