Question

The derivative of $\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ with respect to $\sin ^{-1}\left(3 x-4 x^{3}\right)$ is

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

Answer: (A)

Let $y=\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$
and $z=\sin ^{-1}\left(3 x-4 x^{3}\right)$
$\Rightarrow y=2 \sin ^{-1} x$ and $z=3 \sin ^{-1} x$
$\Rightarrow y=\frac{2}{3} z$
$\therefore \frac{d y}{d z}=\frac{2}{3}$