Answer
$$
\frac{\partial z}{\partial t} =\frac{\partial f}{\partial x} \frac{\partial g}{\partial t} +\frac{\partial f}{\partial y} \frac{\partial h}{\partial t} .
$$
Work Step by Step
To find $\frac{\partial z}{\partial t} $ we apply the chain rule as follows
$$
\frac{\partial z}{\partial t} =\frac{\partial f}{\partial x} \frac{\partial g}{\partial t} +\frac{\partial f}{\partial y} \frac{\partial h}{\partial t} .
$$
