# How do you find the derivative of y = cos 2x?

Jan 5, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 2 \sin 2 x$

#### Explanation:

what we have here is a function 2x inside another function cos .

This is known as a function of a function.

If we differentiate cosx we get - sinx

when we differentiate cos2x we get - sin2x but then have to differentiate 2x.

This can be written as y = cos2x

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = - \sin 2 x . \frac{d}{\mathrm{dx}} \left(2 x\right) = - \sin 2 x . 2$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = - 2 \sin 2 x$