[list][*]Use the input box for f(x) to define a function. Use the input box and slider tool for c to adjust the location of the point P along the graph of f(x). [/*][*]Click the "Trace Derivative" button to trace a graph of the derivative function. [/*][*]Use the checkbox for f'(x) to show / hide the graph of the derivative function. [/*][/list]

The derivative function y = f'(x) is a function whose outputs are the instantaneous rates of change of the function f(x). In other words, to get the output f'(x), look at the slope of the tangent line on the graph of f(x). [br][br]Using the graphing tool above we can look at the graphs of the derivative of some common functions. If we recognize the graph of the derivative function, we may be able to make an educated guess about the formula for the derivative function. By doing so, we can define a rule for differentiating this type of function. [This is a very informal process for "proving" derivative formulas.]