In this talk, we expand on Taylor Series by finding the optimal rational function to approximate a function near a point. We'll see how the controlable limiting behavior of rational functions make Padé Approximants extreamly adventagous, and how the Padé Approximant "agrees" with Taylor expansion. We'll also see how Taylor Series, along with a generalization of the power rule to complex values (using the gamma function), can be used to find the half derivitive, the -pi th derivitive, or the 1+i th derivitive of any function. We'll finish by exploring properties of surfaces where the z value above (x,y) is the yth order derivitive evaluate at x.