# What is the derivative of cos(xy)?

Jan 13, 2017

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

#### Explanation:

Use the chain rule:

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

then the product rule:

$- \sin \left(x y\right) \cdot \frac{d}{\mathrm{dx}} \left(x y\right) = - \sin \left(x y\right) \left(y + x \frac{\mathrm{dy}}{\mathrm{dx}}\right)$