Answer
False.
Work Step by Step
Correct solution:
$u=\sin{2x}$; $\dfrac{du}{dx}=2\cos{2x}$
$\dfrac{d}{du}f(u)=2u$
$\dfrac{d}{dx}f(x)=\dfrac{d}{du}f(u)\times\dfrac{du}{dx}=4\cos{2x}\sin{2x}.$
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