Answer
$$\frac{dy}{dt}=\pi\sin(2\pi t-4)$$
Work Step by Step
According to the Chain Rule: $$\frac{dy}{dt}=\frac{d}{dt}\sin^2(\pi t-2)=2\sin(\pi t-2)\frac{d}{dt}\sin(\pi t-2)$$
$$\frac{dy}{dt}=2\sin(\pi t-2)\cos(\pi t-2)\frac{d}{dt}(\pi t-2)$$
$$\frac{dy}{dt}=2\sin(\pi t-2)\cos(\pi t-2)(\pi\times1-0)$$
$$\frac{dy}{dt}=2\pi\sin(\pi t-2)\cos(\pi t-2)$$
Recall the identity $2\sin A\cos A=\sin2A$: $$\frac{dy}{dt}=\pi\sin(2\pi t-4)$$