The number e and the exponential e^x are defined and explained. Also, the inverse of the natural logarithm is discovered and explained with graphs and animations. Properties of the natural logarithm and the exponential function are explained. Several examples of finding the derivative of e^u for various u functions are shown. We also see how to sketch the graph of f(x) = x^2e^-x. A really great, comprehensive video on logarithms.