1.50: Product rule and small increments

0606/12/O/N/18 — Question 4 · 5 marks

It is given that y=x3ln(2x+1)y = x^{3}\ln(2x + 1).
(i)
Find the value of dydx\dfrac{\mathrm{d}y}{\mathrm{d}x} when x=0.3x = 0.3. You must show all your working.
[4]
(ii)
Hence find the approximate increase in yy when xx increases from 0.30.3 to 0.3+h0.3 + h, where hh is small.
[1]