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The derivative of the function/ arccos*sqrt(x)

Derivative of arccos*sqrt(x)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
          ___
acos(x)*\/ x
xacos⁡(x)\sqrt{x} \operatorname{acos}{\left(x \right)} 
acos(x)*sqrt(x)
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
               ___   
acos(x)      \/ x    
------- - -----------
    ___      ________
2*\/ x      /      2 
          \/  1 - x
−x1−x2+acos⁡(x)2x- \frac{\sqrt{x}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2 \sqrt{x}}
Simplify
The second derivative [src] 
 /                         3/2             \
 |        1               x         acos(x)|
-|----------------- + ----------- + -------|
 |         ________           3/2       3/2|
 |  ___   /      2    /     2\       4*x   |
 \\/ x *\/  1 - x     \1 - x /             /
−(x32(1−x2)32+1x1−x2+acos⁡(x)4x32)- (\frac{x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{4 x^{\frac{3}{2}}})
Simplify
The third derivative [src] 
                                                         /          2 \
                                                     ___ |       3*x  |
                                                   \/ x *|-1 + -------|
         ___                                             |           2|
     3*\/ x               3            3*acos(x)         \     -1 + x /
- ------------- + ------------------ + --------- + --------------------
            3/2             ________        5/2                3/2     
    /     2\         3/2   /      2      8*x           /     2\        
  2*\1 - x /      4*x   *\/  1 - x                     \1 - x /
x(3x2x2−1−1)(1−x2)32−3x2(1−x2)32+34x321−x2+3acos⁡(x)8x52\frac{\sqrt{x} \left(\frac{3 x^{2}}{x^{2} - 1} - 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3 \sqrt{x}}{2 \left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{4 x^{\frac{3}{2}} \sqrt{1 - x^{2}}} + \frac{3 \operatorname{acos}{\left(x \right)}}{8 x^{\frac{5}{2}}}
Simplify
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