# What is the derivative of  sin (x/2)?

Aug 1, 2016

$\frac{1}{2} \cos \left(\frac{x}{2}\right)$

#### Explanation:

We use the chain rule, as we have $y \left(u \left(x\right)\right)$

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

$u = \frac{x}{2} \implies \frac{\mathrm{du}}{\mathrm{dx}} = \frac{1}{2}$

$y = \sin \left(u\right) \implies \frac{\mathrm{dy}}{\mathrm{du}} = \cos \left(u\right)$

$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(u\right) \cdot \frac{1}{2} = \frac{1}{2} \cos \left(\frac{x}{2}\right)$