1.67: Quotient rule and small increments

0606/13/M/J/19 — Question 4 · 5 marks

It is given that y=ln⁡(2x3+5)x−1y = \dfrac{\ln(2x^{3} + 5)}{x - 1} for x>1x > 1.
(i)
Find the value of dydx\dfrac{\mathrm{d}y}{\mathrm{d}x} when x=2x = 2. You must show all your working.
[4]
(ii)
Find the approximate change in yy as xx increases from 22 to 2+p2 + p, where pp is small.
[1]