What is the derivative of a function?
The derivative of a function at a given point is the slope of the tangent line to the graph of the function at that point. It can be approximated by the ratio of finite increments in y and x, and the approximation improves the smaller the increments. In the figure below, click and drag the lower point to change where the derivative is being calculated. Click and drag the upper point to change the size of the increments used to calculate the derivative. Notice how the slope of the red line approximates the slope of the blue tangent line as the points are brought closer together.