1.84: Quotient rule and related rates

Given that $y = \dfrac{\mathrm{e}^{2x - 3}}{x^{2} + 1}$, find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$.

Hence, given that $y$ is increasing at the rate of $2$ units per second, find the exact rate of change of $x$ when $x = 2$.