Answer
$\dfrac{dy}{dx}=\dfrac{\cos{x}}{4\sin{2y}}.$
Work Step by Step
$\dfrac{d}{dx}(\sin{x})+2\dfrac{d}{dx}(\cos{2y})=\dfrac{d}{dx}(1)\rightarrow$
$\cos{x}+\dfrac{dy}{dx}(-4\sin{2y})=0\rightarrow$
$\dfrac{dy}{dx}=\dfrac{\cos{x}}{4\sin{2y}}.$