Visual Calculus - Definition of Derivative

Problem:
Using the definition of derivative, calculate the derivative of

Visualization:
The following LiveMath notebook shows the steps you would follow in doing this problem. You can change the value of the coefficients. View an animation to see how this can be done.

The correct mathematical notation for writing the next to last line in the original notebook is

Comment: The main reason that the LiveMath notebook appears so complicated is that the program wants to cancel out the terms f(x + h) + f(x) early in computations. The extra steps in the notebook prevents this from happening.