Производная acos(5*x)^3

Вы ввели

    3     
acos (5*x)

$$\operatorname{acos}^{3}{\left (5 x \right )}$$

Первая производная

        2     
-15*acos (5*x)
--------------
   ___________
  /         2 
\/  1 - 25*x  

$$- \frac{15 \operatorname{acos}^{2}{\left (5 x \right )}}{\sqrt{- 25 x^{2} + 1}}$$

Вторая производная

    /    2        5*x*acos(5*x) \          
-75*|---------- + --------------|*acos(5*x)
    |         2              3/2|          
    |-1 + 25*x    /        2\   |          
    \             \1 - 25*x /   /          

$$- 75 \left(\frac{5 x \operatorname{acos}{\left (5 x \right )}}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2}{25 x^{2} - 1}\right) \operatorname{acos}{\left (5 x \right )}$$

Третья производная

    /                         2              2     2                      \
    |        2            acos (5*x)     75*x *acos (5*x)   30*x*acos(5*x)|
375*|- -------------- - -------------- - ---------------- + --------------|
    |             3/2              3/2               5/2                2 |
    |  /        2\      /        2\       /        2\       /         2\  |
    \  \1 - 25*x /      \1 - 25*x /       \1 - 25*x /       \-1 + 25*x /  /

$$375 \left(- \frac{75 x^{2} \operatorname{acos}^{2}{\left (5 x \right )}}{\left(- 25 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{30 x \operatorname{acos}{\left (5 x \right )}}{\left(25 x^{2} - 1\right)^{2}} - \frac{\operatorname{acos}^{2}{\left (5 x \right )}}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{2}{\left(- 25 x^{2} + 1\right)^{\frac{3}{2}}}\right)$$