How are the floor area of a room, its length, and its width related to each other? ([See Fig. 8.])
The answer is told in any one of three equations:
(floor area) equals (length) times (width)
(length) equals (floor area) divided by (width)
(width) equals (floor area) divided by (length)
The first equation shows that the floor area depends on the length of the room and also on the width of the room. So we say floor area is a function of length and width. This particular function happens to be product, the result of multiplication. In other words, floor area is equal to the product of length and width.
Now there is another kind of function called a differential function or derivative. A differential function or derivative is an instantaneous rate of change. An instantaneous rate of change is the result of two steps: (1) finding a rate of change over an interval and then (2) letting the interval become smaller and smaller indefinitely. For example, suppose that we have the problem:
How are speed, distance, and time related to each other?
One of the answers is:
(speed) equals the instantaneous rate of change of (distance) with respect to (time)