Whenever a function y=f(x) has a specific interpretation in one of the sciences, its derivative will have a specific interpretation as a rate of change .

Example: If s=f(t) measures displacment as a function of time, then the derivative has unit length/time, which is velocity. A second differentiation yields length/time² or acceleration.

Example: If m=f(x) measures the mass of a wire (as a function of position), then the derivative has units of mass/length or density.

Example: If Q=f(t) measures charge as a function of time in a circuit, then the derivative has units of charge/time, or current.

Other examples can be found in

• Biology
• Chemistry
• Economics
• Physiology
• Thermodynamics

In fact, since nearly all the problems of science or engineering involve functions as well as changes in time of physical quantities, many of the most important equations include derivatives (differential equations).

Last modified Wed Sep 18 20:59:23 CDT 1996