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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.
PROJECT FILES
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