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The derivative of the function/ arcsin(√x)+√(x-x^2)

Derivative of arcsin(√x)+√(x-x^2)

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

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The solution

You have entered [src] 
                 ________
    /  ___\     /      2 
asin\\/ x / + \/  x - x
$$\sqrt{- x^{2} + x} + \operatorname{asin}{\left(\sqrt{x} \right)}$$ 
asin(sqrt(x)) + sqrt(x - x^2)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1/2 - x             1        
----------- + -----------------
   ________       ___   _______
  /      2    2*\/ x *\/ 1 - x 
\/  x - x
$$\frac{\frac{1}{2} - x}{\sqrt{- x^{2} + x}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x}}$$
Simplify
The second derivative [src] 
                                                 2                        
        1                1             (-1 + 2*x)               1         
- ------------- - ---------------- - ---------------- + ------------------
    ___________      3/2   _______                3/2       ___        3/2
  \/ x*(1 - x)    4*x   *\/ 1 - x    4*(x*(1 - x))      4*\/ x *(1 - x)
$$- \frac{1}{\sqrt{x \left(1 - x\right)}} - \frac{\left(2 x - 1\right)^{2}}{4 \left(x \left(1 - x\right)\right)^{\frac{3}{2}}} + \frac{1}{4 \sqrt{x} \left(1 - x\right)^{\frac{3}{2}}} - \frac{1}{4 x^{\frac{3}{2}} \sqrt{1 - x}}$$
Simplify
The third derivative [src] 
                               3                                                       
  12*(-1 + 2*x)    3*(-1 + 2*x)            2                3                 3        
- -------------- - -------------- - --------------- + -------------- + ----------------
             3/2              5/2    3/2        3/2    5/2   _______     ___        5/2
  (x*(1 - x))      (x*(1 - x))      x   *(1 - x)      x   *\/ 1 - x    \/ x *(1 - x)   
---------------------------------------------------------------------------------------
                                           8
$$\frac{- \frac{12 \left(2 x - 1\right)}{\left(x \left(1 - x\right)\right)^{\frac{3}{2}}} - \frac{3 \left(2 x - 1\right)^{3}}{\left(x \left(1 - x\right)\right)^{\frac{5}{2}}} + \frac{3}{\sqrt{x} \left(1 - x\right)^{\frac{5}{2}}} - \frac{2}{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}} \sqrt{1 - x}}}{8}$$
Simplify
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