If a mathematical equation describes some physical quantity as a function of time, the derivative of that equation describes the rate of change as a function of time.
For example, if the motion of a car can be described as:
Then at any time (
This also applies to cases where the velocity is not constant. The motion of a projectile thrown straight up will be described by:
The derivative will give you the velocity as a function of
But it's not limited to equations of motion. If you ask about decay rates of radioactive material, I can right down a function for the number of atoms at any given time:
And the rate at which I see atoms decay will be: