Approximating and Guessing Derivative
How this applet works
In this applet you can plug in the function you would like to guess the derivative of in the f(x) field. You can then approximate this derivative using the limit definition of the derivative by using the slider to examine different values of h as h goes to zero. Finally, you can guess a formula for the derivative by entering a function in the "Guess for Derivative" field. Then you can examine if your formula is what you are looking for!