EITHER: Use chain rule
obtain $\frac{{dx}}{{dt}} = 6\sin t\cos t$, or equivalent
obtain $\frac{{dy}}{{dt}} = - 6{\cos ^2}t\sin t$, or equivalent
Use $\frac{{dy}}{{dx}} = \frac{{dy}}{{dt}} \div \frac{{dx}}{{dt}}$
OR: Express $y$ in terms of $x$ and use chain rule
Obtain $\frac{{dy}}{{dx}} = k{(2 - \frac{x}{3})^{\frac{1}{2}}}$, or equivalent
Obtain $\frac{{dy}}{{dx}} = - {(2 - \frac{x}{3})^{\frac{1}{2}}}$, or equivalent
Express derivative in terms of $t$
Obtain final answer $\frac{{dy}}{{dx}} = - \cos t$