Производная cos(2*acos(x))

Вы ввели

cos(2*acos(x))

$$\cos{\left (2 \operatorname{acos}{\left (x \right )} \right )}$$

Первая производная

2*sin(2*acos(x))
----------------
     ________   
    /      2    
  \/  1 - x     

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

Вторая производная

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

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

Третья производная

  /                    2                                    \
  |  sin(2*acos(x))   x *sin(2*acos(x))   2*x*cos(2*acos(x))|
6*|- -------------- + ----------------- - ------------------|
  |           3/2                5/2                   2    |
  |   /     2\           /     2\             /      2\     |
  \   \1 - x /           \1 - x /             \-1 + x /     /

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