# How do you find the derivative of 1/2sin2x?

Apr 5, 2018

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

#### Explanation:

we will use the chain rule

$\frac{\mathrm{dy}}{\mathrm{dx}} = \textcolor{red}{\frac{\mathrm{dy}}{\mathrm{du}}} \frac{\mathrm{du}}{\mathrm{dx}}$

$y = \frac{1}{2} \sin 2 x$

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

$\textcolor{red}{y = \frac{1}{2} \sin u \implies \frac{\mathrm{dy}}{\mathrm{du}} = \frac{1}{2} \cos u}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \textcolor{red}{\frac{1}{2} \cos u} \times x 2$

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