**Ch 2 - Derivatives**

**Chapter 2 PDF Resource**

calculus_chapter_2.pdf |

**Lecture Notes & Videos**

Graphical Representation: Slope of the Secant Line

-----VIDEO: Demonstration of a Secant Line Approaching a Tangent Line

Section 2-1 (Day 1)

The Derivative & The Tangent Line Problem

-----VIDEO: How the Difference Quotient Connects to the Slope of the Tangent Line

-----VIDEO: Using the Limit Definition, Find the Slope of the Tangent Line at a Given Point

-----VIDEO: The Limit Definition of a Derivative

Various Notations for the Derivative

-----VIDEO: Derivative Notation: Lagrange, Leibniz, Euler, and Newton

Section 2-1 (Day 2)

A Graphical Approach to Derivatives

-----VIDEO: Analyzing the Derivative Graphically in Beginning Calculus

Vertical Tangents, Cusps & Differentiability

-----VIDEO: Vertical Tangent Line Demonstration

Six Cases Where a Function is NOT Differentiable

-----VIDEO: 6 Cases Where a Function is NOT Differentiable

Section 2-2

Power Rule

-----VIDEO: Using the nDeriv Function on the TI-84

-----VIDEO: Power Rule for Derivatives

Applications of the Derivative

Velocity & Acceleration

-----VIDEO: Position ◆ Velocity ◆ Acceleration in Beginning Calculus

Section 2-3 (Day 1)

Product & Quotient Rules and Trig Functions

-----VIDEO: Product Rule for Derivatives

-----VIDEO: Extended Product Rule

-----VIDEO: Quotient Rule for Derivatives

Section 2-3 (Day 2)

Higher Order Derivatives

The Normal Line

-----VIDEO: Writing the Equation of the Normal Line

Solving Equations Using The Rational Root Theorem

-----VIDEO: Solving Equations Using the Rational Root Theorem

Section 2-4 (Day 1)

The Chain Rule

Chain Rule Formula

-----VIDEO: Chain Rule in Calculus 1

Section 2-4 (Day 2)

Trig Functions & The Chain Rule

-----VIDEO: Trig Derivatives with Multiple Chain Rules

-----VIDEO: 4 Examples of Trig Derivatives with Chain Rule

-----VIDEO: Tricks for Memorizing Trig Derivatives

Section 2-4 (Day 3)

More Practice with Finding the Equation of the Tangent Line

-----VIDEO: Finding the Equation of the Tangent Line

-----VIDEO: How to Draw and Find the Equation of the Tangent Line on the TI-84

Derivatives & Graphing Examples

Derivatives & Graphing (In-Class Worksheet for Day 3 Lecture over Sec 2-4)

Derivatives Involving Absolute Value, Symbolic Differentiation, Differentiation from Tables

-----VIDEO: AP Calculus AB Topic: Symbolic Differentiation

Section 2-5 (Day 1)

Implicit Differentiation

-----VIDEO: Short Introduction to Implicit Differentiation

-----VIDEO: Two Examples of Implicit Differentiation

-----VIDEO: Two Harder Examples of Implicit Differentiation

Section 2-5 (Day 2)

More on Implicit Differentiation

-----VIDEO: Finding the 2nd Derivative using Implicit Differentiation

Section 2-6 (Day 1 and 2)

Related Rates

Light Pole Explanation

-----VIDEO: A Prerequisite Skill for Related Rates: Implicitly Differentiating with Respect to Time

-----VIDEO: Related Rates - Pebble Dropped in a Pond

-----VIDEO: Related Rates - Balloon Being Pumped Up

-----VIDEO: Related Rates - Ladder Problem

-----VIDEO: Related Rates - Inverted Cone Problem - Water Leaking Out

-----VIDEO: Related Rates - Shadow Problem - Man Walking Toward Light

-----VIDEO: Demonstration of a Secant Line Approaching a Tangent Line

Section 2-1 (Day 1)

The Derivative & The Tangent Line Problem

-----VIDEO: How the Difference Quotient Connects to the Slope of the Tangent Line

-----VIDEO: Using the Limit Definition, Find the Slope of the Tangent Line at a Given Point

-----VIDEO: The Limit Definition of a Derivative

Various Notations for the Derivative

-----VIDEO: Derivative Notation: Lagrange, Leibniz, Euler, and Newton

Section 2-1 (Day 2)

A Graphical Approach to Derivatives

-----VIDEO: Analyzing the Derivative Graphically in Beginning Calculus

Vertical Tangents, Cusps & Differentiability

-----VIDEO: Vertical Tangent Line Demonstration

Six Cases Where a Function is NOT Differentiable

-----VIDEO: 6 Cases Where a Function is NOT Differentiable

Section 2-2

Power Rule

-----VIDEO: Using the nDeriv Function on the TI-84

-----VIDEO: Power Rule for Derivatives

Applications of the Derivative

Velocity & Acceleration

-----VIDEO: Position ◆ Velocity ◆ Acceleration in Beginning Calculus

Section 2-3 (Day 1)

Product & Quotient Rules and Trig Functions

-----VIDEO: Product Rule for Derivatives

-----VIDEO: Extended Product Rule

-----VIDEO: Quotient Rule for Derivatives

Section 2-3 (Day 2)

Higher Order Derivatives

The Normal Line

-----VIDEO: Writing the Equation of the Normal Line

Solving Equations Using The Rational Root Theorem

-----VIDEO: Solving Equations Using the Rational Root Theorem

Section 2-4 (Day 1)

The Chain Rule

Chain Rule Formula

-----VIDEO: Chain Rule in Calculus 1

Section 2-4 (Day 2)

Trig Functions & The Chain Rule

-----VIDEO: Trig Derivatives with Multiple Chain Rules

-----VIDEO: 4 Examples of Trig Derivatives with Chain Rule

-----VIDEO: Tricks for Memorizing Trig Derivatives

Section 2-4 (Day 3)

More Practice with Finding the Equation of the Tangent Line

-----VIDEO: Finding the Equation of the Tangent Line

-----VIDEO: How to Draw and Find the Equation of the Tangent Line on the TI-84

Derivatives & Graphing Examples

Derivatives & Graphing (In-Class Worksheet for Day 3 Lecture over Sec 2-4)

Derivatives Involving Absolute Value, Symbolic Differentiation, Differentiation from Tables

-----VIDEO: AP Calculus AB Topic: Symbolic Differentiation

Section 2-5 (Day 1)

Implicit Differentiation

-----VIDEO: Short Introduction to Implicit Differentiation

-----VIDEO: Two Examples of Implicit Differentiation

-----VIDEO: Two Harder Examples of Implicit Differentiation

Section 2-5 (Day 2)

More on Implicit Differentiation

-----VIDEO: Finding the 2nd Derivative using Implicit Differentiation

Section 2-6 (Day 1 and 2)

Related Rates

Light Pole Explanation

-----VIDEO: A Prerequisite Skill for Related Rates: Implicitly Differentiating with Respect to Time

-----VIDEO: Related Rates - Pebble Dropped in a Pond

-----VIDEO: Related Rates - Balloon Being Pumped Up

-----VIDEO: Related Rates - Ladder Problem

-----VIDEO: Related Rates - Inverted Cone Problem - Water Leaking Out

-----VIDEO: Related Rates - Shadow Problem - Man Walking Toward Light

**Worksheets**

Velocity & Acceleration Applications WS

Trig Limits Review WS

Differentiability WS #1

Cumulative Review WS (Ch 1 thru Sec 2-3)

Cumulative Review WS (Ch 1 thru Sec 2-3) KEY

Tangent & Normal Line WS

Solving Equations Using The Rational Root Theorem WS

Derivatives & Graphing (In-Class Worksheet for Day 3 Lecture over Sec 2-4)

Differentiation Review WS #1

Absolute Value Derivatives WS

Differentiation from Tables & Symbolically WS

More Practice with Trig Derivatives WS

Symbolic Differentiation WS

Differentiation Review WS #2

Differentiating with Respect to Time WS

Related Rates WS #1

Chapter 2 Review Concepts WS

Chapter 1 Review WS

Chapter 1 Review WS KEY

Related Rates WS #2

Related Rates WS #2 KEY

Miscellaneous Review WS

Miscellaneous Review WS KEY

Trig Limits Review WS

Differentiability WS #1

Cumulative Review WS (Ch 1 thru Sec 2-3)

Cumulative Review WS (Ch 1 thru Sec 2-3) KEY

Tangent & Normal Line WS

Solving Equations Using The Rational Root Theorem WS

Derivatives & Graphing (In-Class Worksheet for Day 3 Lecture over Sec 2-4)

Differentiation Review WS #1

Absolute Value Derivatives WS

Differentiation from Tables & Symbolically WS

More Practice with Trig Derivatives WS

Symbolic Differentiation WS

Differentiation Review WS #2

Differentiating with Respect to Time WS

Related Rates WS #1

Chapter 2 Review Concepts WS

Chapter 1 Review WS

Chapter 1 Review WS KEY

Related Rates WS #2

Related Rates WS #2 KEY

Miscellaneous Review WS

Miscellaneous Review WS KEY

**Study Guides**

**(Used Prior to 2021-22)**

**Interactive Animations**

Calculus is the study of change. The ability to change a parameter and immediately see the result can demonstrate that change and how things are related during that change. Many of these concepts are much easier to explain if that change, the motion, can be visually demonstrated in class. Therefore, this is a perfect place for the use of computer animations.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

**Please be patient! It takes awhile for these to load.**

Widen the browser, if necessary, to see the entire animation.

Widen the browser, if necessary, to see the entire animation.

**Tangent Line Sliding Along the Function**

**Zooming in on a Tangent Line**

This animation is a version of the common demonstration that a smooth curve becomes indistinguishable from its tangent line when viewed under a sufficiently high power microscope.

**Vertical Tangent Line - A Point of Non-Differentiability**

This is a pretty straightforward interactive animation depicting the geometric convergence of a tangent line to a vertical tangent line, where at that point, the derivative does not exist. The slope of the tangent (which converges to the derivative) is also displayed.

**Falling Ladder - Related Rates Demo**

As you can see, the speed of the bottom of the ladder at point A is constant, but the speed of the top of the ladder at point B changes. This is a demo from Stewart's Calculus, Concepts and Contexts, 4th Edition.

**Cone - Related Rates Demo**

As you can see, the cone fills faster at the beginning and then slows down the closer it gets to the top.

**Light Pole - Related Rates Demo**

In the distance versus time plot notice that DistHomerPlot (which is the distance Homer is from the lamp post at time t) is a straight line.

- Why is it a line?
- What is the slope of this line?

- Why is it a line?
- What is the slope of this line?

Homer Simpson, who is 6 ft tall, is walking away from a 18 ft tall lamp post at a speed of 8 ft/s. How fast is the tip of his shadow moving along the ground when he is 100 ft from the lamp post?