of a function $f(x)$ at a point $a$ measures the slope
of the tangent line to the function at that point. To help
visualize the derivative, imagine the function as a wave that you
are surfing. The tilt of your surf board is the slope.
In the applet below we have two windows. The top window displays the graph of the function in the text box. (You can change this if you wish to) As you move point $a$ along the graph, your "surf board" changes to match the slope of the curve, and a triangle is created with base length of 1 and height equal to the slope. This height is then plotted in the bottom window as a function. The bottom window thus graphs the derivative.