About This Chapter
Computing Derivatives - Chapter Summary and Learning Objectives
The video lessons in this Computing Derivatives chapter are designed to help you understand the use of higher order derivatives as well as the chain rule when solving equations. The lessons cover topics such as the derivative of perpetual motion and implicit differentiation. They also explain the steps for finding the first, second, third and fourth derivatives. The chapter includes self-assessment quizzes and an examination that can help you solidify your understanding of the following:
|Calculating Derivatives of Trigonometric Functions||Explain the steps for calculating the derivative of trigonometric functions.|
|Calculating Derivatives of Polynomial Equations||Examine the power rule for derivatives and learn to find the derivatives of polynomial functions.|
|Using the Chain Rule to Differentiate Complex Functions||Simplify nesting equations with the chain rule.|
|Differentiating Factored Polynomials: Product Rule and Expansion||Explore the rules for multiplying functions and solving with the product rule.|
|Understanding Higher Order Derivatives Using Graphs||Discover the steps for calculating higher order derivatives.|
|Calculating Higher Order Derivatives||Learn the applications of mathematical jerk, acceleration and velocity when calculating higher order derivatives.|
|How to Find Derivatives of Implicit Functions||Explore implicit functions and discuss the steps involved in implicit differentiation.|
|How to Calculate Derivatives of Inverse Trigonometric Functions||Explore derivative formulas for inverse trigonometric functions.|
|Applying the Rules of Differentiation to Calculate Derivatives||Discuss the rules for solving common derivatives.|
|Calculating Derivatives of Exponential Equations||Learn to calculate derivatives of exponentials and the rate of an exponential's change.|
1. Finding Derivatives of Sums, Products, Differences & Quotients
This lesson will go over how to find the derivative of a sum, difference, product, and quotient. We will look at the different formulas involved in these derivatives and use those formulas to calculate some derivatives.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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)!
9. 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.
10. 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.
11. 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.
12. Calculating Derivatives of Logarithmic Functions
Logarithms appear in all types of applications like carbon dating, brightness of stars and musical acoustics. In this lesson we explore how to calculate the derivative of logarithmic functions.
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Other chapters within the AP Calculus AB: Exam Prep course
- Graph Basics
- The Basics of Functions
- How to Graph Functions
- Limits of Functions
- Continuity of Functions
- Understanding Exponentials & Logarithms
- Using Exponents and Polynomials
- Properties of Derivatives
- The Derivative at a Point
- The Derivative as a Function
- Second Derivatives
- Using Derivatives
- Properties of Definite Integrals
- Applications of Integrals
- Using the Fundamental Theorem of Calculus
- Understanding & Applying Integration Techniques
- Approximating Definite Integrals
- Using a Scientific Calculator for Calculus
- About the AP Calculus Exam
- AP Calculus AB Flashcards