What is the area, A, of a rectangle, if it has length L and width W?
The answer is simple: A=LxW.
So the area increases if the length L increases or if the width W increases. The area depends on two variables: the length and the width.
Now we can ask: how rapidly does A change if we change one of those variables? In other words, at what rate does A change?
For a function that depends on only one variable, we can differentiate to find the rate at which that function changes, and we can do just the same for a function of two (or more) variables, like A above.
We'll come back to A later, but first let's look at a slightly more complicated function of two variables.