Derivative/Definition

The derivative of a function is defined as the instantaneous rate of change of the function at a certain point. For a line, this is just the slope. For more complex curves, we can find the rate of change between two points on the curve easily since we can draw a line through them.

In the image above, the rate of change between the two points is the slope of the line that goes through them: .

We can move the second point closer to the first one to find a more accurate value of the derivative. Thus, taking the limit as goes to 0 will give us the derivative of the function at :

See also

• Calculus
• Derivative