SOLUTION —
$\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2} \Rightarrow \sin ^{-1} x=\frac{\pi}{2}-\sin ^{-1} y$
$\Rightarrow \quad \sin ^{-1} x=\cos ^{-1} y \Rightarrow y=\sqrt{1-x^2}$
$\Rightarrow \quad \frac{d y}{d x}=\frac{1}{2 \sqrt{1-x^2}}(-2 x)=-\frac{x}{y}$
So, The correct option will be (B).