1.20: Show that where and are integers to be found

4PM1/1/June/2023 — Question 2 · 5 marks

y = (\mathrm{sin} 2x) \sqrt{3 + 2x}

Show that

\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{sin} 2x + (A + Bx) \mathrm{cos} 2x}{\sqrt{3 + 2x}}

where

\displaystyle A

and

\displaystyle B

are integers to be found.

(5)