About This Chapter
Derivative Rules - Chapter Summary
If you need to brush up on derivative rules, this chapter is designed to help you recall that information with easy-to-understand and bite-size lessons. You will study information about the relationship between the derivative and Super C, discover how constant multiples and additions relate to derivatives and find out how to calculate the derivative. By the time you reach the end of these lessons, you should be ready to:
- Identify how to find the slope of a function
- Explore how to graph the derivative on a graph of a function
- Describe the rate of change
- Explain the quotient rule and its use
By reviewing these topics, which are presented to you in an organized and engaging manner, you could become more prepared to solve derivative problems on your own. The video lessons are short and informative. Each lesson is between five to ten minutes long, and each has multiple-choice quizzes so that you can test yourself on what you are learning. That way you can find out what your weak areas are, then go back to the lessons and re-study the material.
1. Derivatives: The Formal Definition
The derivative defines calculus. In this lesson, learn how the derivative is related to the instantaneous rate of change with Super C, the cannonball man.
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. 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.
4. Derivatives: Graphical Representations
Take a graphical look at the definitive element of calculus: the derivative. The slope of a function is the derivative, as you will see in this lesson.
5. Graphing the Derivative from Any Function
When you know the rules, calculating the derivates of equations is relatively straightforward, although it can be tedious! What happens, though, when you don't know the function? In this lesson, learn how to graph the derivative of a function based solely on a graph of the function!
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. 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.
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- Calculations & Applications of Derivatives
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