Производная cos(asin(x)/2)

Вы ввели

   /asin(x)\
cos|-------|
   \   2   /

$$\cos{\left (\frac{1}{2} \operatorname{asin}{\left (x \right )} \right )}$$

Первая производная

    /asin(x)\ 
-sin|-------| 
    \   2   / 
--------------
     ________ 
    /      2  
2*\/  1 - x   

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

Вторая производная

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

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

Третья производная

   /   /asin(x)\          /asin(x)\      2    /asin(x)\\
   |sin|-------|   2*x*cos|-------|   4*x *sin|-------||
   |   \   2   /          \   2   /           \   2   /|
-3*|------------ + ---------------- + -----------------|
   |        3/2                2                 5/2   |
   |/     2\          /      2\          /     2\      |
   \\1 - x /          \-1 + x /          \1 - x /      /
--------------------------------------------------------
                           8                            

$$- \frac{1}{8} \left(\frac{12 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} \sin{\left (\frac{1}{2} \operatorname{asin}{\left (x \right )} \right )} + \frac{6 x}{\left(x^{2} - 1\right)^{2}} \cos{\left (\frac{1}{2} \operatorname{asin}{\left (x \right )} \right )} + \frac{3}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \sin{\left (\frac{1}{2} \operatorname{asin}{\left (x \right )} \right )}\right)$$

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