Additional Mathematics 4037/22 — May/June 2011

Given that $y = \sin 3x$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$.

Hence find the approximate increase in $y$ as $x$ increases from $\frac{\pi}{9}$ to $\frac{\pi}{9} + p$, where $p$ is small.