Unit 4 - Sections 3.1 to 3.3

Module Overview

In this unit, we begin our study of derivatives. We begin by defining them as a type of limit and trying to understand what they say about functions. Then, we try to figure out how to evaluate derivatives without the use of limits.

Learning Outcomes

We begin by defining the derivative and trying to find what it says about the original function. We then try to understand the derivative as a function itself.
Section 3.1 ends by examining more closely the behaviour of the derivative, as well as a crucial requirement for its existence.
In Section 3.2, we find that the derivative for many simple functions can be found using mechanical methods far easier and faster than using the limit definition.
Section 3.3 introduces two rules that allow us to significantly expand the list of functions whose derivative we can take without using limits directly.

Type: Video Links
Title	Author	Description
Derivatives - Introduction \| Derivatives - Introduction	Shai Cohen
Derivatives - A First Example \| Derivatives - A First Example	Shai Cohen
Derivatives - A Second Look \| Derivatives - A Second Look	Shai Cohen
Derivatives - A Third Approach \| Derivatives - A Third Approach	Shai Cohen
Derivatives Example - First Principles Derivative \| Derivatives Example - First Principles Derivative	Shai Cohen
Derivatives Example - First Principles Derivative: Medium \| Derivatives Example - First Principles Derivative: Medium	Shai Cohen
Derivatives Example - First Principles Derivative: Hard pt. 1 \| Derivatives Example - First Principles Derivative: Hard pt. 1	Shai Cohen
Derivatives Example - First Principles Derivative: Hard pt. 2 \| Derivatives Example - First Principles Derivative: Hard pt. 2	Shai Cohen
Derivatives Example - First Principles Derivative: Hard pt. 3 \| Derivatives Example - First Principles Derivative: Hard pt. 3	Shai Cohen
Derivatives Example - Derivatives From Graphs 1 \| Derivatives Example - Derivatives From Graphs 1	Shai Cohen
Derivatives Example - Derivatives From Graphs 2 \| Derivatives Example - Derivatives From Graphs 2	Shai Cohen
Derivatives - From the Graph \| Derivatives - From the Graph	Shai Cohen
Derivatives - The Tangent Line \| Derivatives - The Tangent Line	Shai Cohen
Derivatives - Tangent Lines \| Derivatives - Tangent Lines	Shai Cohen
Derivatives - Differentiability and Continuity \| Derivatives - Differentiability and Continuity	Shai Cohen
Rules for Derivatives - Higher Order Derivatives \| Rules for Derivatives - Higher Order Derivatives	Shai Cohen
Rules for Derivatives - Derivative Rules \| Rules for Derivatives - Derivative Rules	Shai Cohen
The Power Rule Example - A Formal Proof \| The Power Rule Example - A Formal Proof	Shai Cohen
Higher-Order Derivatives Example - nth Derivative \| Higher-Order Derivatives Example - nth Derivative	Shai Cohen
Product and Quotient Rules - Product Rule \| Product and Quotient Rules - Product Rule	Shai Cohen
Product and Quotient Rules - Quotient Rule \| Product and Quotient Rules - Quotient Rule	Shai Cohen
Product Rule Example - Silly Uses \| Product Rule Example - Silly Uses	Shai Cohen
Quotient Rule Example - The Quotient Rule and Higher Order Derivatives \| Quotient Rule Example - The Quotient Rule and Higher Order Derivatives	Shai Cohen
Derivatives - The First Three Sections \| Derivatives - The First Three Sections	Shai Cohen