Definition of Derivative
The blue line shown below is the tangent line at the point on the graph of . You can use the "a" slider to move the location of that point.
The orange line is a secant line passing through the point and a second point nearby on the graph of . You can use the "h" slider to change how far the second point is from the first. Notice that the orange secant line looks more and more like the blue tangent line as h approaches 0.
The slope of the secant line is the difference quotient, and the slope of the tangent line is the derivative, which is the limit of the difference quotient as h approaches 0.