It has been said that you are your own worst enemy, and the same can certainly be said about ex. To demonstrate, let's graph the difference quotient for f(x)=e^x using an infinitesimal value of h. Duration: 4:54

Before we formally derive the differentiation rule for e^x, let's go to an extremely generous bank to review the limit definition of e. Duration: 9:43

With some clever substitution, we can develop an alternate limit definition for e. Instead of a limit at infinity, this one will be super close to zero. Duration: 4:56

Now that we have assembled all of the necessary pieces, let's prove that e^x is its own worst enemy, I mean, its own derivative. Duration: 14:28

Example 13 reiterates the fact that the y-values on the graph of f(x)=e^x give the slope of the graph at a given point. Duration: 2:53

Finally, on Example 14, we will continue to make connections between the graph of a function and its derivative, as well as get a preview of how the second derivative shapes a graph. Duration: 6:22