Differentiation

Abstract

In our work so far we have developed the integral and discussed the process of integration at some length. The calculus is built around two concepts of which integration is only one. The other part of the calculus will investigate the rate at which a function changes. One of the important questions concerning any thing that is changing is “How fast is it changing?” This is just as true in matters of economic and social change as it is for change of location or change in the amount of your mathematical knowledge since you first opened this book. It is this question which we wish to address in this chapter. We shall find that it has very far reaching ramifications, and that there are many rather subtle matters that must be considered. We shall be more alert to the nature of the ideas involved, however, than the rigorous treatment of the subtleties in this chapter. We shall come back to consider the latter in more detail in Chapter VII.