# How do you find the derivative of cos(pi x)?

Aug 14, 2018

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

#### Explanation:

Let,

$y = \cos \left(\pi x\right)$

Using Chain Rule :

$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = - \sin \left(\pi x\right) \frac{d}{\mathrm{dx}} \left(\pi x\right)$

$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = - \sin \left(\pi x\right) \left(\pi\right)$

$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = - \pi \sin \left(\pi x\right)$