Introduction to Derivatives In this chapter we will be understand what a derivative is, how to tell if it exists or not, and how to find it if it Summary: Chapter 3 Introduction to Derivatives In this chapter we will be understand what a derivative is, how to tell if it exists or not, and how to find it if it does. The ideas of limits and continuity of a function are pillars on which we build the derivative so we begin with those concepts. Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be. ­ Bertrand Russell Yet in another way, calculus is fundamentally naive, almost childish in its optimism. Experience teaches us that change can be sudden, dis- continuous, and wrenching. Calculus draws its power by refusing to see that. It insists on a world without accidents, where one thing leads log- ically to another. Give me the initial conditions and the law of motion, and with calculus I can predict the future ­ or better yet, reconstruct the past. I wish I could do that now. ­Steven Strogatz Calculus has its limits. ­ Anon. 3.1 Limits and Continuity Collections: Mathematics