Производная cos(10*acos(x))

Вы ввели

cos(10*acos(x))

$$\cos{\left (10 \operatorname{acos}{\left (x \right )} \right )}$$

Первая производная

10*sin(10*acos(x))
------------------
      ________    
     /      2     
   \/  1 - x      

$$\frac{10}{\sqrt{- x^{2} + 1}} \sin{\left (10 \operatorname{acos}{\left (x \right )} \right )}$$

Вторая производная

   /10*cos(10*acos(x))   x*sin(10*acos(x))\
10*|------------------ + -----------------|
   |           2                    3/2   |
   |     -1 + x             /     2\      |
   \                        \1 - x /      /

$$10 \left(\frac{x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \sin{\left (10 \operatorname{acos}{\left (x \right )} \right )} + \frac{10}{x^{2} - 1} \cos{\left (10 \operatorname{acos}{\left (x \right )} \right )}\right)$$

Третья производная

   /                        2                                       \
   |  33*sin(10*acos(x))   x *sin(10*acos(x))   10*x*cos(10*acos(x))|
30*|- ------------------ + ------------------ - --------------------|
   |             3/2                  5/2                     2     |
   |     /     2\             /     2\               /      2\      |
   \     \1 - x /             \1 - x /               \-1 + x /      /

$$30 \left(\frac{x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} \sin{\left (10 \operatorname{acos}{\left (x \right )} \right )} - \frac{10 x}{\left(x^{2} - 1\right)^{2}} \cos{\left (10 \operatorname{acos}{\left (x \right )} \right )} - \frac{33}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \sin{\left (10 \operatorname{acos}{\left (x \right )} \right )}\right)$$