Answer
$\frac{dy}{dx}=\frac{1}{\sqrt{(1-x^2)}}$
Work Step by Step
Given $x=\sin{y}$, differentiate the equation with respect to x:
$1=\cos{y}\frac{dy}{dx}$
$\frac{dy}{dx}=\frac{1}{\cos{y}}$
$\cos{y}=\sqrt{(1-\sin^2{y})}=\sqrt{(1-x^2)}$
$\frac{dy}{dx}=\frac{1}{\sqrt{(1-x^2)}}$
