3.22: Derivative of ln quotient at x = 0

0606/12/M/J/25 — Question 8 · 6 marks · Exponentials, Log laws

It is given that y=ln⁡(3x2+16)x+2y = \dfrac{\ln(3x^{2} + 16)}{x + 2}.
(a)
Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x} when x=0x = 0. Give your answer in the form ln⁡p\ln p, where pp is a constant.
[5]
(b)
Given that xx increases from 00 to hh, where hh is small, write down the approximate change in yy.
[1]