The Derivative as a Function

If we set f'(x) to be the derivative of f(x) at x, i.e. the slope of the tangent line to f(x) at x = a, we can create a new function called the derivative which is defined everywhere that the limit lim_(h->0) (f(x+h) - f(x))/h exists.

Drag the point x back and forth to trace out the graph of y = f'(x).

Type "f(x) = ___" to redefine f(x) as a new function.

Jason McCullough, Created with GeoGebra