# Ch 7: Calculating Derivatives and Derivative Rules: Help and Review

### About This Chapter

## Who's it for?

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

- Students who have fallen behind in understanding calculating derivatives or working with the rules of differentiation
- 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 chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any calculating derivatives or derivative rules question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

In this chapter, you'll learn the answers to questions including:

- How can I use limits to compute a derivative?
- What are the two major properties found in derivatives?
- How can I calculate the derivative of an exponential or a polynomial equation?
- What steps do I use to calculate the derivative of a trigonometric function?
- How can I use the chain rule to differentiate complex functions?
- What are higher order derivatives, and how do I calculate them?

### 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. How to Take the Derivative of tan(x)

In this lesson we show how to take the derivative of the tangent function including the cases when the argument is a function of x. As an application, we show how this derivative is used for approximating a function.

### 15. Taking the Derivative of arcsin: How-To & Tutorial

In this lesson, the derivative of arcsin x is determined using a reference triangle and the chain rule. These ideas are extended by plotting arcsin x and then using the derivative result to draw the tangent line.

### 16. How to Take the Derivative of x^2: Steps & Tutorial

Getting the basics right is important! In this lesson, you will learn how to find the derivative of the relatively simple term x^2. You'll see the underlying method that lets you solve the derivatives of expressions of any power and you'll also learn how to verify that your answer is correct.

### 17. Calculating the Derivative of ln(x)^2

In this lesson, we will learn two methods for finding the derivative of the natural logarithm of x-squared. This result is also obtained by using logarithm properties and the definition of the derivative using limits.

### 18. What is the Derivative of xy? - How-To & Steps

Read this how-to lesson and you'll see how easy it is to find the derivative of xy. You'll learn the single step that you need to take along with the two rules that are used in this single step.

### 19. Finding the Derivative of x^4: How-To & Steps

In this lesson we show the short way to find the derivative of x^4 and then verify this result using the limits definition of the derivative. As an application, we look at the formula describing the power radiated by the earth.

### 20. Taking the Derivative of e^4x: How-To & Steps

In this lesson, we show how to take the derivative of an exponential where the argument of the exponential is a specific function of x. After explaining the steps, we verify the result using graphical examples.

### 21. Finding the Derivative of ln(x)/x: How-To & Steps

In this lesson, we will see how to use the quotient rule for derivatives to find the derivative of ln(x) / x. After we find out this derivative, we will see how to it might be used in a real world application.

### 22. Taking the Derivative of ln(x)^x: How-To & Steps

In this lesson, we use a property of logarithms and their derivatives as well as the chain rule to find the derivative of the logarithm of x raised to the x power.

### 23. Taking the Derivative of 5x^2: How-To & Steps

In this lesson, we will find the derivative of 5x^2. We will learn a general formula we can use to find this derivative and we will also look at how to use the limit definition of the derivative to find this derivative as well.

### 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 Calculus: Help and Review course

- Graphing and Functions: Help and Review
- Continuity in Calculus: Help and Review
- Geometry and Trigonometry in Calculus: Help and Review
- Using Scientific Calculators in Calculus: Help and Review
- Limits in Calculus: Help and Review
- Rate of Change in Calculus: Help and Review
- Graphing Derivatives and L'Hopital's Rule: Help and Review
- Applications of Derivatives: Help and Review
- Area Under the Curve and Integrals: Help and Review
- Integration and Integration Techniques: Help and Review
- Integration Applications: Help and Review
- Differential Equations: Help and Review