Answer
$$
\frac{dz}{dt}=\frac{\partial z}{\partial x} \frac{d x}{dt}+\frac{\partial z}{\partial y} \frac{d y}{dt}.
$$
Work Step by Step
To find $\frac{dz}{dt}$ we apply the chain rule as follows
$$
\frac{dz}{dt}=\frac{\partial z}{\partial x} \frac{d x}{dt}+\frac{\partial z}{\partial y} \frac{d y}{dt}.
$$
