# Ch 10: Calculus - Derivatives Calculations & Rules: Help & Review

### About This Chapter

## Who's It For?

Anyone who needs help learning or mastering AP calculus material will benefit from taking this course. There is no faster or easier way to learn AP calculus. Among those who would benefit are:

- Students who have fallen behind in understanding derivative calculations and rules
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about calculating derivatives and derivative rules
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How It Works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the calculating derivatives and derivative rules chapter exam.

## Why it works:

**Study Efficiently:**Skip what you know; review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the calculating derivatives and derivative rules in AP calculus chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any question on derivative calculations and rules. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in a calculating derivatives and derivative rules unit of a standard AP Calculus AB and BC course. Topics covered include:

- Using limits to calculate the derivative
- Calculating derivatives of trigonometric, polynomial and exponential equations
- Using the chain rule
- Differentiating factored polynomials
- Using graphs to understand higher order derivatives
- Calculating higher order derivatives
- Finding derivatives of implicit functions
- Calculating derivatives of inverse trigonometric functions

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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)!

### 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.

### 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.

### 14. Product Rule in Calculus: Formula & Examples

In this lesson, you will see how the product rule helps you when taking the derivative of certain functions. Learn how to easily identify the situations in which you can use this rule to help you.

### 15. Undetermined Coefficients: Method & Examples

The method of undetermined coefficients is used to solve a class of nonhomogeneous second order differential equations. This method makes use of the characteristic equation of the corresponding homogeneous differential equation.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the AP Calculus AB & BC: Help and Review course

- Functions in AP Calculus: Help and Review
- Graphing and Functions in AP Calculus: Help and Review
- Sequences and Series in AP Calculus: Help and Review
- Limits in AP Calculus: Help and Review
- Continuity in AP Calculus: Help and Review
- Exponentials and Logarithms in AP Calculus: Help and Review
- Exponents and Polynomials in AP Calculus: Help and Review
- Applications of Derivatives in AP Calculus: Help and Review
- Calculating Derivatives & Derivative Rules in AP Calculus: Help & Review
- Differential Equations in AP Calculus: Help and Review
- Area Under the Curve and Integrals in AP Calculus: Help and Review
- L'Hopital's Rule & Graphing Derivatives: Help & Review
- Integration Applications in AP Calculus: Help and Review
- Rate of Change in AP Calculus: Help and Review
- Geometry and Trigonometry in AP Calculus: Help and Review
- How to Use Scientific Calculators for AP Calculus: Help and Review