d d x [ ^ -1 x- ^ -1 x ] is equal to - Vidyadip

Question

$\frac{d}{d x}\left[\sin ^{-1} x-\sin ^{-1} \sqrt{x}\right]$ is equal to

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Answer

$\text { (c) : Let } y=\frac{d}{d x}\left[\sin ^{-1} x-\sin ^{-1} \sqrt{x}\right]$
$=\frac{1}{\sqrt{1-x^2}}-\frac{1}{2 \sqrt{x} \sqrt{1-x}}=\frac{1}{\sqrt{1-x^2}}-\frac{1}{2 \sqrt{x(1-x)}}$

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