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Ch 9: Calculating Derivatives & Derivative Rules - AP Calculus: Homeschool Curriculum

About This Chapter

The Calculating Derivatives and Derivative Rules unit of this AP Calculus Homeschool course is designed to help homeschooled students learn about related graphs and properties. Parents can use the short videos to introduce topics, break up lessons and keep students engaged.

Who's it for?

This unit of our AP Calculus Homeschool course will benefit any student who is trying to learn about calculating derivatives and derivative rules. There is no faster or easier way to learn about calculus. Among those who would benefit are:

  • Students who require an efficient, self-paced course of study to learn to use differentiation to find minimum and maximum values.
  • Homeschool parents looking to spend less time preparing lessons and more time teaching.
  • Homeschool parents who need a calculus curriculum that appeals to multiple learning types (visual or auditory).
  • Gifted students and students with learning differences.

How it works:

  • Students watch a short, fun video lesson that covers a specific unit topic.
  • Students and parents can refer to the video transcripts to reinforce learning.
  • Short quizzes and a Calculating Derivatives and Derivative Rules unit exam confirm understanding or identify any topics that require review.

Calculating Derivatives and Derivative Rules Unit Objectives:

  • Define L'Hopital's Rule.
  • Learn how to apply L'Hopital's Rule.
  • Determine concavity and inflection points.
  • Learn to graph the derivative from any function.
  • Discuss data mining.
  • Study non-differentiable graphs of derivatives.

13 Lessons in Chapter 9: Calculating Derivatives & Derivative Rules - AP Calculus: Homeschool Curriculum
Test your knowledge with a 30-question chapter practice test
Using Limits to Calculate the Derivative

1. Using Limits to Calculate the Derivative

If you know the position of someone as a function of time, you can calculate the derivative -- the velocity of that person -- as a function of time as well. Use the definition of the derivative and your knowledge of limits to do just that in this lesson.

The Linear Properties of a Derivative

2. The Linear Properties of a Derivative

In this lesson, learn two key properties of derivatives: constant multiples and additions. You will 'divide and conquer' in your approach to calculating the limits used to find derivatives.

Calculating Derivatives of Trigonometric Functions

3. Calculating Derivatives of Trigonometric Functions

The trigonometric functions show up almost everywhere that you have a repeating pattern. In this lesson, learn how to find the derivatives of the trigonometric functions.

Calculating Derivatives of Polynomial Equations

4. Calculating Derivatives of Polynomial Equations

Polynomials can describe just about anything and are especially common in describing motion. Learn the tricks to quickly finding the derivatives of these ubiquitous functions.

Calculating Derivatives of Exponential Equations

5. Calculating Derivatives of Exponential Equations

Earth's population is booming! But why is the population increasing so much more drastically than it did many years ago? In this lesson, learn how to calculate the rates of change in exponentials by discovering the rules of derivatives with exponents.

Using the Chain Rule to Differentiate Complex Functions

6. Using the Chain Rule to Differentiate Complex Functions

If you've ever seen a complicated function, this lesson is for you. Most functions that we want to differentiate are complicated functions, for which no single derivative rule will work. In this lesson, learn how to use the chain rule to simplify nesting equations.

Differentiating Factored Polynomials: Product Rule and Expansion

7. Differentiating Factored Polynomials: Product Rule and Expansion

Most functions that we want to differentiate are complicated functions for which no single derivative rule will work. In this lesson, learn what happens to derivatives when you multiply functions together.

When to Use the Quotient Rule for Differentiation

8. When to Use the Quotient Rule for Differentiation

Lo D Hi minus Hi D Lo, all over the square of what's below! Learn the quotient rule chant for differentiating functions that take the form of fractions in this lesson.

Understanding Higher Order Derivatives Using Graphs

9. Understanding Higher Order Derivatives Using Graphs

The derivative is a rate of change, like velocity. What happens, though, when your velocity - that is, your rate of change - is changing? Explore the changing changes in this lesson.

Calculating Higher Order Derivatives

10. Calculating Higher Order Derivatives

Differentiating functions doesn't have to stop with the first or even second derivative. Learn what a mathematical jerk is as you calculate derivatives of any order in this lesson.

How to Find Derivatives of Implicit Functions

11. How to Find Derivatives of Implicit Functions

How do you define the rate of change when your function has variables that cannot be separated? Learn how implicit differentiation can be used to find dy/dx even when you don't have y=f(x)!

How to Calculate Derivatives of Inverse Trigonometric Functions

12. How to Calculate Derivatives of Inverse Trigonometric Functions

Like a metronome, trigonometric functions are regular. Even predictable. In this lesson, you will learn how to use this predictability to remember the derivative formulas for these common functions.

Applying the Rules of Differentiation to Calculate Derivatives

13. Applying the Rules of Differentiation to Calculate Derivatives

In this lesson, we'll review common derivatives and their rules, including the product, quotient and chain rules. We'll also examine how to solve derivative problems through several examples.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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