3.36: Ln quotient: derivative and rates

0606/13/M/J/24 — Question 6 · 7 marks

It is given that y=ln(2x2+1)x+2y = \dfrac{\ln(2x^{2} + 1)}{x + 2}, x>2x > -2.
(a)
Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}.
[3]
(b)
Given that xx increases from 11 to 1+h1 + h, where hh is small, find the approximate corresponding change in yy.
[2]
(c)
When x=1x = 1, the rate of change in yy is 33 units per second. Find the corresponding rate of change in xx.
[2]