About This Chapter
Differentiation in Calculus - Chapter Summary
The process of studying differentiation in calculus has never been easier thanks to the resources in this chapter. Explore fun lessons developed by expert instructors to boost your understanding of the applications of differentiation and derivatives. Upon completion of this chapter, you'll be ready to do the following:
- Differentiate complex functions using the chain rule
- Describe when to use the quotient rule and product rules in calculus
- Calculate derivatives by applying the rules of differentiation
- Find the derivatives of trigonometric functions and the second derivative
- Define the mean value theorem, and use Rolle's theorem
- Use differentiation to calculate minimum and maximum values
The flexibility of this chapter enables you to study whenever and wherever you have time. Lessons and other resources are accessible 24/7 and can be reviewed on any device with an Internet connection. Use the lessons to enhance your knowledge of differentiation in calculus, and take multiple-choice quizzes to assess your comprehension. If you hit a snag while examining the lessons and need additional information, don't hesitate to submit your questions to our experts.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. Finding the Second Derivative: Formula & Examples
In this lesson, you will learn the two-step process involved in finding the second derivative. Also, look at some examples to get your feet wet before jumping into the quiz.
7. What is the Mean Value Theorem?
Three people set off on a car trip. They all start at the same time and end at the same time. Learn what calculus says about how fast they traveled along the way as you study the Mean Value Theorem in this lesson.
8. Rolle's Theorem: A Special Case of the Mean Value Theorem
Super C, the human cannonball, is shot into the air at 35 mph, but his average vertical velocity is zero. In this lesson, you will use Rolle's theorem to explain what this means about Super C's flight.
9. Using Differentiation to Find Maximum and Minimum Values
If you are shot out of a cannon, how do you know when you've reached your maximum height? When walking through a valley, how do you know when you are at the bottom? In this lesson, use the properties of the derivative to find the maxima and minima of a function.
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