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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
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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