1.76: Product rule and small increments

0606/13/O/N/17 — Question 8 · 8 marks

It is given that y=(x4)(3x1)53y = (x - 4)(3x - 1)^{\frac{5}{3}}.
(i)
Show that dydx=(3x1)23(Ax+B)\dfrac{\mathrm{d}y}{\mathrm{d}x} = (3x - 1)^{\frac{2}{3}}(Ax + B), where AA and BB are integers to be found.
[5]
(ii)
Hence find, in terms of hh, where hh is small, the approximate change in yy when xx increases from 33 to 3+h3 + h.
[3]