I am trying to expand $\sqrt{x(1-x)}$ in order to find the order of it as $x\to0$.

Using Taylor expansion to find the derivative of the equation as $x\to0$ gives each item $0$.

Then how do we expand it? Thanks,
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my answer: 

$\sqrt{x(1-x)}$

$=x^{1/2}(1-x)^{1/2}$ 

expand for $x\to 0$, 

$=x^{1/2}(1+\frac 12(-x)+\frac{\frac12(1-\frac{1}{2})}{2!}(-x)^2+...........)$ 

$=x^{1/2}-\frac 12x^{3/2}-\frac{1}{8}x^{5/2}+...........$
As Aditya Agarwal said:

$\sqrt{x(1+x)}=x^{1/2}(1-x/2+...)$