Lesson Plan: Definition of the Derivative Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to calculate the derivative of a function using the formal definition of the derivative as a limit.

Objectives

Students will be able to

• understand that the derivative of a function at a point represents the slope of the tangent to the function at this point,
• calculate the derivatives of polynomial functions using the definition of a derivative in terms of a limit,
• calculate the derivatives of other algebraic functions, such as radical functions or rational functions with 1 as a numerator, using the definition of a derivative in terms of a limit,
• identify the derivative notations (including prime and Leibniz’s notation).

Prerequisites

Students should already be familiar with

• evaluating functions,
• finding the domain and range of functions,
• graphing functions,
• finding limits.

Exclusions

Students will not cover

• finding the derivative using the power rule for derivatives.