Chapter 4 Symbolic Differentiation
In the last chapter we approximated derivatives by using a balanced difference quotient. For most functions that gave an easy approximation without any rules other than the conceptual understanding that we obtained the derivative by zooming in far enough for the graph to look like a straight line. When we looked at the derivative at many points we found that for polynomials of degree 2 or less, the derivative seems to be a polynomial of one degree lower. In this chapter we explore rules for symbolic differentiation. This lets us move from a function defined by a formula to its derivative defined by a formula without going through the work of finding best fitting curves. It also will work with a many functions where Excel will not have the appropriate choice available if we want to fit a curve.