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

## dy/dx = -2sin2x ##

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

## rArr dy/dx = - sin2x . d/dx (2x )= - sin2x . 2 ##

##rArr dy/dx = -2sin2x ##