Question

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

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

Answer 1

Answer: (A)

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