Chapter 4: Inverse Functions. Higher Derivatives. Exponential and Logarithmic Functions

Introduction

The derivative of a derivative is called a second derivative. For motion, the second derivative of positionis acceleration.

The inverse function, g, to f satisfies g(f(x))=x in some domain.

We explore the properties of exponentials and their inverses: logarithms.

Topics

4.1 Inverse Functions

4.2 Higher Derivatives

4.3 The Exponential Function

4.4 The Natural Logarithm

4.5 Other Powers

4.6 Logarithms to other Bases