Answer
$h'(x)=2\cos{4x}.$
Work Step by Step
You can use the product rule to differentiate but it would be much easier to use the identity $(2\sin{x}\cos{x}=\sin{2x})$ to rewrite $h(x)$ as $\dfrac{\sin{4x}}{2}$
$u=4x$; $\dfrac{du}{dx}=4$
$\dfrac{d}{du}h(u)=\dfrac{\cos{u}}{2}$
$\dfrac{d}{dx}h(x)=\dfrac{d}{du}h(u)\times\dfrac{du}{dx}=2\cos{4x}.$
