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

MCQ

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

A
$\frac{1}{2 \sqrt{x(1-x)}}-\frac{1}{\sqrt{1-x^2}}$
B
$\frac{1}{\sqrt{1-\left\{x \sqrt{1-x}-\sqrt{\left.x\left(1-x^2\right)\right\}^2}\right.}}$
✓
$\frac{1}{\sqrt{1-x^2}}-\frac{1}{2 \sqrt{x(1-x)}}$
D
$\frac{1}{\sqrt{x(1-x)(1-x)^2}}$

✓

Answer

Correct option: C.

$\frac{1}{\sqrt{1-x^2}}-\frac{1}{2 \sqrt{x(1-x)}}$

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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