Prove that : \[ \frac{d}{d x}\left(\cos ^{-1} \sqrt{\frac{1+x}{2}}\...

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Prove that :
\[
\frac{d}{d x}\left(\cos ^{-1} \sqrt{\frac{1+x}{2}}\right)=\frac{-1}{2 \sqrt{1-x^{2}}} \text { for }-1x1
\]
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