If $x = \sin y$, what is $\frac{dy}{dx}$ in terms of $x$?

Explanation

1. 01

   Differentiate with respect to $x$: $1 = \cos y\frac{dy}{dx}$, so $\frac{dy}{dx} = \frac{1}{\cos y}$.

2. 02

   $\cos y = \sqrt{1 - \sin^2 y} = \sqrt{1 - x^2}$ (taking $\cos y > 0$), so $\frac{dy}{dx} = \frac{1}{\sqrt{1 - x^2}}$.