3.12: Quotient of ln and linear: rates of change

0606/22/F/M/25 — Question 6 · 8 marks

It is given that y=ln(2x2+1)x+2y = \dfrac{\ln(2x^{2} + 1)}{x + 2}.
(a)
Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}.
[3]
(b)
Given that xx increases from 22 to 2+h2 + h, where hh is small, find the approximate change in yy.
[2]
(c)
Given that yy is decreasing by 0.40.4 units per second, find the corresponding rate of change in xx when x=2x = 2.
[3]