3.59: Derivative of product and normal

Given that $y = 4\,\mathrm{sin}\,x\,\mathrm{cos}^{2} x$, find the value of $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ when $x = \dfrac{\pi}{6}$.

A curve has equation $y = 4\,\mathrm{sin}\,x\,\mathrm{cos}^{2} x$. The normal to the curve at the point where $x = \dfrac{\pi}{6}$ meets the $x$-axis at the point $P$. Find the exact coordinates of $P$.