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Ch 25: TExES Physics/Math 7-12: Derivatives & Differentiation in Calculus

About This Chapter

Explore derivatives and differentiation in calculus in preparation for taking the TExES Physics/Math 7-12 examination for teacher certification. This chapter consists of online tutorial video lessons and a practice chapter test.

TExES Physics/Math 7-12: Derivatives & Differentiation in Calculus - Chapter Summary

Prior to taking the TExES Physics/Math 7-12 examination, brush up on your understanding of derivatives and differentiation. This chapter's video lessons allow you to revisit techniques for writing derivatives, differentiating functions, calculating the rate of change and implementing the quotient rule. You can also gather more information about the use of the chain rule and the power rule. View the videos in order to:

  • Learn more about the fundamentals of derivatives
  • Explain limits, differentiability and graphical representations
  • Discover when to apply the quotient rule
  • Differentiate using the quotient rule
  • Understand and apply the product rule
  • Explore the use of technology when solving differential equations

You'll have unlimited access to these instructor-delivered video lessons, which are presented online. Just use your wired or mobile technology and study at your own pace. All of the animated lessons have navigational video tags that will take you instantly from one topic to the next. Find these topics by clicking on the Timeline feature. The videos can be paused or watched again, and the quizzes can be taken more than once. You might even print them out for use as offline study tools. Written transcripts are included in the chapter.

7 Lessons in Chapter 25: TExES Physics/Math 7-12: Derivatives & Differentiation in Calculus
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.

Using Limits to Calculate the Derivative

2. 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.

Derivatives: Graphical Representations

3. 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'

4. 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.

When to Use the Quotient Rule for Differentiation

5. 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.

Differentiating Factored Polynomials: Product Rule and Expansion

6. 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.

Solving Differential Equations & Integrals with Technology

7. Solving Differential Equations & Integrals with Technology

Solving for differential equations and integrals can often be a complex and time-consuming process. In this lesson, a scientific graphing calculator (Texas Instruments TI-84) will be used to graphically solve for both the derivative and the integral.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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