Use the indicated buttons and input boxes to explore different functions and their derivatives. When you press the "Animate a" button, you will see different values being traced for the derivative of your function.
You can show the graph of the derivative function by using the check box (especially helpful if you are exploring other functions, and the trace only comes out as dots).
Use the input bar to change the function.
The dynamic text below the function bar will tell you the function being graphed, as well as its derivative.

How does does the graph of f ' (x) appear to be related to f(x), when f(x)=sinx?
Take hold of the graph f(x) and move it up in the cartesian plane (or in the input box, add a constant [for example: sin(x) + 2])...how does this effect the derivative?
Input a different function, and watch the animation of its derivative. How is the graph of this derivative f ' (x) related to the f(x) that you chose?