Производная e^((asin(x))^4)

Вы ввели

     4   
 asin (x)
E        

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

Первая производная

                4   
      3     asin (x)
4*asin (x)*e        
--------------------
       ________     
      /      2      
    \/  1 - x       

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

Вторая производная

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

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

Третья производная

  /                    2              8             4         2     2                             5   \              4   
  |     6          asin (x)    16*asin (x)   36*asin (x)   3*x *asin (x)   9*x*asin(x)   12*x*asin (x)|          asin (x)
4*|----------- + ----------- + ----------- + ----------- + ------------- + ----------- + -------------|*asin(x)*e        
  |        3/2           3/2           3/2           3/2            5/2              2              2 |                  
  |/     2\      /     2\      /     2\      /     2\       /     2\        /      2\      /      2\  |                  
  \\1 - x /      \1 - x /      \1 - x /      \1 - x /       \1 - x /        \-1 + x /      \-1 + x /  /                  

$$4 \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}^{5}{\left (x \right )}}{\left(x^{2} - 1\right)^{2}} + \frac{9 x \operatorname{asin}{\left (x \right )}}{\left(x^{2} - 1\right)^{2}} + \frac{16 \operatorname{asin}^{8}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{36 \operatorname{asin}^{4}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{\operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) e^{\operatorname{asin}^{4}{\left (x \right )}} \operatorname{asin}{\left (x \right )}$$