# How do you differentiate f(x)= sin2xcos2x using the product rule?

Jul 19, 2017

$f ' \left(x\right) = 2 \cos 4 x$

#### Explanation:

Using the trig identity:

$\sin 2 A \equiv 2 \sin A \cos A$

We have:

$\sin 4 A \equiv 2 \sin 2 A \cos 2 A$

So we can write:

$f \left(x\right) = \sin 2 x \cos 2$
$\text{ } = \frac{1}{2} \sin 4 x$

And so, using the chain rule we have:

$f ' \left(x\right) = \frac{1}{2} \cos 4 x \cdot 4$
$\text{ } = 2 \cos 4 x$

This is an easier method than using the product rule