Question

How do I find the derivative of `f(x) = sin(2x)cos(2x)`?

Answer 1

Either use the product rule and the chain rule or apply a trig identity and only use the chain rule.

Explanation:

Personally I prefer the latter option:

I would use the double angle formula:
`sin(2theta)=2sin(theta)cos(theta)`

Trasforming you equation into:
`f(x) = 1/2 sin(4x)`

Which can then be differentiated using the chain rule:
Multiply by the derivative of the bracket and differentiate the trig term:
`f'(x) = (4)*1/2*cos(4x)`
`=> f'(x) = 2cos(4x)`

If you want to know the other method, search the 'product rule' in your search engine of choice.