# How do you find dx/dy given y=sinx+cosx?

Dec 17, 2016

$\frac{\mathrm{dx}}{\mathrm{dy}} = \frac{1}{\cos x - \sin x}$

#### Explanation:

$y = \sin x + \cos x$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \cos x - \sin x$

By the chain rule $\frac{\mathrm{dx}}{\mathrm{dy}} = \frac{1}{\frac{\mathrm{dy}}{\mathrm{dx}}}$

$\therefore \frac{\mathrm{dx}}{\mathrm{dy}} = \frac{1}{\cos x - \sin x}$