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Chapter 6: Differentiable Functions, the Derivative and Differentials

Introduction

We introduce the notion of differentiability, discuss the differentiability of standard functions and examples of non-differentiable behavior. We then describe differentiability of a function of two variables, directional derivatives, partial derivatives the tangent plane and the gradient. Some philosophic implications are also discussed.

Topics

6.1 Differentiability, the Tangent Line-Linear Approximation

6.2 Differentiability of Standard Functions

6.3 Examples of non Differentiable Behavior

6.4 Derivatives in Two Dimensions: Directional Derivative and Partial Derivatives

6.5 The Tangent Plane and the Gradient Vector

6.6 The Gradient and Directional Derivatives

6.7 Philosophic Implications