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The derivative of the function/ arccos^(3)5x

Derivative of arccos^(3)5x

Function f() - derivative -N order at the point
v

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The solution

You have entered [src] 
    3     
acos (5*x)
$$\operatorname{acos}^{3}{\left(5 x \right)}$$ 
acos(5*x)^3
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        2     
-15*acos (5*x)
--------------
   ___________
  /         2 
\/  1 - 25*x
$$- \frac{15 \operatorname{acos}^{2}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
Simplify
The second derivative [src] 
    /    2        5*x*acos(5*x) \          
-75*|---------- + --------------|*acos(5*x)
    |         2              3/2|          
    |-1 + 25*x    /        2\   |          
    \             \1 - 25*x /   /
$$- 75 \left(\frac{5 x \operatorname{acos}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{25 x^{2} - 1}\right) \operatorname{acos}{\left(5 x \right)}$$
Simplify
The third derivative [src] 
    /                         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 /  /
$$375 \left(- \frac{75 x^{2} \operatorname{acos}^{2}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{30 x \operatorname{acos}{\left(5 x \right)}}{\left(25 x^{2} - 1\right)^{2}} - \frac{\operatorname{acos}^{2}{\left(5 x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}\right)$$
Simplify
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