Ch 9: Overview of Properties of Derivatives

About This Chapter

Master the properties of derivatives and the concepts used in calculating and representing them. This chapter covers the definition of derivatives and the basics of using them in your calculus work. Use our helpful videos to boost your learning.

Overview of Properties of Derivatives - Chapter Summary

Review the lessons in this chapter for an overview of the basic principles behind using derivatives in calculus. You can gain a better understanding of what it means to be 'differentiable' and study how to calculate these derivatives. You'll also see examples of the linear properties of derivatives, review when to use the quotient rule and explore optimization and differentiation.

After you complete the chapter, you should be able to:

  • Explain what derivatives are and how they define calculus
  • Understand and create a graphical representation of the slope of a function
  • Describe the meaning of the term 'differentiable' and how it applies to calculus
  • Use limits, such as position, to calculate velocity as a function of time
  • Define constant multiples and additions and demonstrate their application in calculating limits
  • Identify a continuous function and the relationship between continuity and differentiability

Our lessons are accessible from your computer and mobile device so you can study anywhere, at your convenience. Take advantage of the tools offered in this chapter, including video lessons with full transcripts and lesson quizzes, to track your progress and help the information stick.

8 Lessons in Chapter 9: Overview of Properties of Derivatives
Test your knowledge with a 30-question chapter practice test
Derivatives: The Formal Definition

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.

Derivatives: Graphical Representations

2. 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.

What It Means To Be 'Differentiable'

3. What It Means To Be 'Differentiable'

Lots of jets can go from zero to 300 mph quickly, but super-jets can do this instantaneously. In this lesson, learn what that means for differentiability.

Using Limits to Calculate the Derivative

4. 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.

The Linear Properties of a Derivative

5. 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.

When to Use the Quotient Rule for Differentiation

6. 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.

The Relationship Between Continuity & Differentiability

7. The Relationship Between Continuity & Differentiability

Why is it that all differentiable functions are continuous but not all continuous functions are differentiable? Learn why in this video lesson. Also see what a continuous function looks like versus one that isn't.

Optimization and Differentiation

8. Optimization and Differentiation

In this lesson, you can learn what optimization means from a mathematical standpoint. Using the techniques taught in this lesson, you can use the five steps to optimization to figure out practical things, like how much sleep you need to get before an exam.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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