Q. The derivative of $\sin^{- 1}{(2x\sqrt{1 - x^{2}}\ )}\$with respect to $\sin^{- 1}{(3x - 4x^{3})}\$is
A) $\frac{2}{3}$
B) $\frac{3}{2}$
C) $\frac{1}{2}$
D) 1
Explanation
(a)
Let $y = \sin^{- 1}{\left( 2x\sqrt{1 - x^{2}} \right)\ and\ \ \ z = \sin^{- 1}{(3x - 4x^{3})}}$
$\Rightarrow \ \ y = 2\sin^{- 1}{x\ \ and\ }\ \ z = 3\sin^{- 1}x$
$\Rightarrow y = \frac{2}{3}\ z\ \ \therefore\frac{dy}{dz} = \frac{2}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.