1.47: Quotient rule with a logarithm

Given that $y = \dfrac{\ln(3x^{2} + 2)}{x^{2} + 1}$, find the value of $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ when $x = 2$, giving your answer as $a + b\ln 14$, where $a$ and $b$ are fractions in their simplest form.