# How do you use implicit differentiation to find dy/dx given xcosy=1?

Mar 16, 2017

#### Explanation:

$\frac{d \left(x \cos \left(y\right)\right)}{\mathrm{dx}} = \frac{d \left(1\right)}{\mathrm{dx}}$

Use the product rule on the left; the right side is 0:

$\cos \left(y\right) - x \sin \left(y\right) \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$x \sin \left(y\right) \frac{\mathrm{dy}}{\mathrm{dx}} = \cos \left(y\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos \frac{y}{x \sin \left(y\right)}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cot \frac{y}{x}$