This applet traces the first derivative of an arbitrary function. Enter a function into the input with a string like 'f(x) = x^3' (which will produce a simple cubic function). The point A is a movable point that will be on the curve and the black line will be a tangent to that curve at the point A. The point D represents the value of the slope of the tangent at the point A. As the point A moves, the point D will trace out a curve that is the derivative of the function f. Finally, you can show the derivative of f by checking the white box in the upper left corner of the frame.
Next enter some other functions to study their derivatives. Some examples might include: sin(2x), exp(x), log(x).
Note that to clear an existing trace, simply reset the zoom on the window.