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

Derivative of arccos(x)^3

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

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The solution

You have entered [src] 
    3   
acos (x)
$$\operatorname{acos}^{3}{\left(x \right)}$$ 
acos(x)^3
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       2   
-3*acos (x)
-----------
   ________
  /      2 
\/  1 - x
$$- \frac{3 \operatorname{acos}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
Simplify
The second derivative [src] 
   /   2       x*acos(x) \        
-3*|------- + -----------|*acos(x)
   |      2           3/2|        
   |-1 + x    /     2\   |        
   \          \1 - x /   /
$$- 3 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x^{2} - 1}\right) \operatorname{acos}{\left(x \right)}$$
Simplify
The third derivative [src] 
  /                      2          2     2                 \
  |       2          acos (x)    3*x *acos (x)   6*x*acos(x)|
3*|- ----------- - ----------- - ------------- + -----------|
  |          3/2           3/2            5/2              2|
  |  /     2\      /     2\       /     2\        /      2\ |
  \  \1 - x /      \1 - x /       \1 - x /        \-1 + x / /
$$3 \left(- \frac{3 x^{2} \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \operatorname{acos}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{\operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$
Simplify
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