Derivatives By Definition

Abstract

An essential step in acquiring mastery of calculus is seeing the derivative as the limit of the slopes of secant lines. This means seeing the derivative as the limit of a difference quotient. One of the obstacles to this understanding is the algebra needed to take the various limits that arise in this context. Let’s explore how Maple can be used to learn about the definition of the derivative without requiring the student to be an algebraic virtuoso. We’ll pick a function, set up the appropriate difference quotient, and explore the idea of the limit.