1.52: Product rule and related rates

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$.

Find the approximate change in $y$ as $x$ increases from $0.5$ to $0.5 + p$, where $p$ is small.

Given that $y$ is increasing at a rate of $2$ units per second when $x = 0.5$, find the corresponding rate of change in $x$.