2.65: Differentiation and small change in a quotient

0606/23/M/J/20 — Question 8 · 8 marks

(a)
Differentiate y=tan(x+4)3sinxy = \tan(x + 4) - 3\sin x with respect to xx.
[2]
(b)
Variables xx and yy are such that y=ln(2x+5)2e3xy = \dfrac{\ln(2x + 5)}{2\mathrm{e}^{3x}}. Use differentiation to find the approximate change in yy as xx increases from 11 to 1+h1 + h, where hh is small.
[6]