2: The Derivative — Read — Invisible Network

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The two previous chapters have laid the foundation for the study of calculus. They provided a review of some material you will need and started to emphasize the various ways we will view and use functions: functions given by graphs, equations and tables of values.

Chapter 2 will focus on the idea of tangent lines. We will develop a definition for the derivative of a function and calculate derivatives of some functions using this definition. Then we will examine some of the properties of derivatives, see some relatively easy ways to calculate the derivatives, and begin to look at some ways we can use them.

2.0: Introduction to Derivatives
2.1: The Definition of Derivative
2.2: Derivatives: Properties and Formulas
2.3: More Differentiation Patterns
2.4: The Chain Rule
2.5: Applications of the Chain Rule
2.6: Related Rates
2.7: Newton’s Method
2.8: Linear Approximation and Differentials
2.9: Implicit and Logarithmic Differentiation
2.A: Answers

This page titled 2: The Derivative was last modified on Wed, 28 Jan 2026 21:00:22 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Dale Hoffman, edited and updated by Jeff Eldridge.

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