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

Mar 8, 2018

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:
$\sin \left(2 \theta\right) = 2 \sin \left(\theta\right) \cos \left(\theta\right)$

Trasforming you equation into:
$f \left(x\right) = \frac{1}{2} \sin \left(4 x\right)$

Which can then be differentiated using the chain rule:
Multiply by the derivative of the bracket and differentiate the trig term:
$f ' \left(x\right) = \left(4\right) \cdot \frac{1}{2} \cdot \cos \left(4 x\right)$
$\implies f ' \left(x\right) = 2 \cos \left(4 x\right)$

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