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.