# How do you find the derivative of  y = sin^2 x?

May 9, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 \sin x \cos x$

#### Explanation:

Using $u = \sin x$ gives us $y = {u}^{2}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

$\frac{\mathrm{dy}}{\mathrm{du}} = 2 u$
$\frac{\mathrm{du}}{\mathrm{dx}} = \cos x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 u \cos x = 2 \sin x \cos x$