One example is water flow. You calculate the rate at which water is being pumped into or drained from a tank, while considering variables such as the changing water level, inflow or outflow rates, and dimensions of the tank.
Also, there's electrical circuits. You're analyzing the changing currents, voltages, or resistances. For example, studying the rate at which the current is changing in an inductor or the rate at which the charge is flowing through a capacitor.
There are many more, but these should give you a good understanding of how multiple variables change with one another and their rates of change.