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

1 Answer
Mar 8, 2018

Answer:

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.