Q. If $y = \sin^{- 1}\sqrt{1 - x},\ then\ \frac{dy}{dx}$ is equal to
A) $\frac{1}{\sqrt{1 - x}}$
B) $\frac{- 1}{2\sqrt{1 - x}}$
C) $\frac{1}{\sqrt{x}}$
D) $\frac{- 1}{2\sqrt{x}\sqrt{1 - x}}$
Explanation
(d)
$y = \sin^{- 1}{\sqrt{1 - x}\ \Rightarrow \frac{dy}{dx}}\ = \frac{1}{\sqrt{1 - (1 - x)}}.\frac{1}{2\sqrt{1 - x}}.( - 1)$
$= \frac{- 1}{2\sqrt{x}\ \sqrt{1 - x}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.