Unit 7 - Sections 3.8, 3.9, 4.1, 4.2

Module Overview

There is quite a bit of material in this unit, starting with a couple of new applications of the Chain Rule and then beginning to study what derivatives actually tell us about functions. This latter part, the beginning of Chapter 4, will allow us to graph functions, optimize them (that is, find maximum and minimum points), and even set up the concept of integration.

Learning Outcomes

Section 3.8: The first of two more applications of the Chain Rule, this section explores how derivatives and logarithms interact. We find the derivative of ln x and also emerge with a new method for integrating functions that would have been impossible at first glance.
Section 3.9: In this final section of applications of the Chain Rule, we use the method that allowed us to find the derivative of logarithms and extend it to inverse trigonometric functions and even general inverse functions.
Section 4.1: The idea behind maximum and minimum points is one of the most important in calculus and its applications. Without the ideas presented here, there would be very few functions where we could figure out their optimal values. What we begin here, we will extend over the next few sections into an understanding of how to graph functions and how to optimize real-world processes.
Section 4.2: We begin Section 4.2 with this unit, looking at the uses of the first derivative in our analysis of functions.

Type: Video Links
Title	Author	Description
Derivatives and Logarithms - The Derivative of ln x \| Derivatives and Logarithms - The Derivative of ln x	Shai Cohen
Derivatives and Logarithms - The Derivative of Other Logarithms \| Derivatives and Logarithms - The Derivative of Other Logarithms	Shai Cohen
Derivatives and Logarithms - Logarithmic Differentiation \| Derivatives and Logarithms - Logarithmic Differentiation	Shai Cohen
Logarithmic Differentiation Example - Easy \| Logarithmic Differentiation Example - Easy	Shai Cohen
Higher-Order Derivatives Example - Logarithms \| Higher-Order Derivatives Example - Logarithms	Shai Cohen
Logarithmic Differentiation Example - A Silly Example \| Logarithmic Differentiation Example - A Silly Example	Shai Cohen
Derivatives and Inverse Functions - The Derivative of Arcsine \| Derivatives and Inverse Functions - The Derivative of Arcsine	Shai Cohen
Derivatives and Inverse Functions - The Derivative of Inverses \| Derivatives and Inverse Functions - The Derivative of Inverses	Shai Cohen
Logarithmic Differentiation Example - With Arc Functions \| Logarithmic Differentiation Example - With Arc Functions	Shai Cohen
Derivative of the Inverse Example \| Derivative of the Inverse Example	Shai Cohen
Maxima and Minima - Absolute \| Maxima and Minima - Absolute	Shai Cohen
Maxima and Minima - Relative \| Maxima and Minima - Relative	Shai Cohen
Maxima and Minima - Extreme Value Theorem \| Extreme Value Theorem	Shai Cohen
Critical Points - an Introduction \| Critical Points - an Introduction	Shai Cohen
Critical Points - the Definition \| Critical Points - the Definition	Shai Cohen
Maxima and Minima - Finding Absolute Extrema \| Maxima and Minima - Finding Absolute Extrema	Shai Cohen
Critical Points Example - Ugly \| Critical Points Example - Ugly	Shai Cohen
Absolute Extrema Example - Intervals \| Absolute Extrema Example - Intervals	Shai Cohen
Uses of the First Derivative - Increasing and Decreasing Intervals \| Uses of the First Derivative - Increasing and Decreasing Intervals	Shai Cohen
Uses of the First Derivative - The First Derivative Test \| Uses of the First Derivative - The First Derivative Test	Shai Cohen
The First Derivative Test - a Second Video \| The First Derivative Test - a Second Video	Shai Cohen
Increasing and Decreasing Example - Polynomial \| Increasing and Decreasing Example - Polynomial	Shai Cohen
Increasing and Decreasing Example - Roots \| Increasing and Decreasing Example - Roots	Shai Cohen
Increasing and Decreasing Example - Ugly \| Increasing and Decreasing Example - Ugly	Shai Cohen
First Derivative Test Example - Polynomial \| First Derivative Test Example - Polynomial	Shai Cohen