ABSTRACT
This chapter begins with the familiar definition of differentiability by considering the canonical example of a function that is continuous everywhere but fails to be differentiable at a point. It proves general rules for differentiating various combinations of the derivatives of some basic functions. The chapter provides some general facts about differentiable functions and proves the familiar rules for differentiating sums, products, and compositions. It discusses the most important application of the derivative to the problem of finding local extrema of functions. The chapter also includes some exercise problems related to the concept of differentiation.
