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Ch 41: FTCE Math: Calculating Derivatives & Derivative Rules

About This Chapter

Review the steps involved in calculating derivatives and derivative rules for the FTCE Math exam. Our expert instructors have prepared a series of engaging video lessons and self-assessment quizzes to quickly get you up to speed.

FTCE Math: Calculating Derivatives & Derivative Rules - Chapter Summary

Prepare for the FTCE math exam with lessons that explore derivatives and derivative rules, including using limits to calculate derivatives, the linear properties of derivatives, and calculating derivatives of trigonometric, polynomial, and exponential equations. In addition, the steps involved in using the chain rule to differentiate complex functions, differentiating factored polynomials, and when to use the quotient rule will be discussed. You'll also cover:

  • Ways to analyze and calculate higher order derivatives with graphs
  • How to calculate derivatives of inverse trigonometric functions
  • Method for using the rules of differentiation to calculate derivatives
  • Related rates

Our expert instructors explain each subject through short, engaging video lessons. The timeline tabs can be used to skip directly to main subjects within the video lessons. Self-assessment quizzes and the chapter exam allow you to gauge your understanding and retention of lesson material.

14 Lessons in Chapter 41: FTCE Math: Calculating Derivatives & Derivative Rules
Test your knowledge with a 30-question chapter practice test
Using Limits to Calculate the Derivative

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.

The Linear Properties of a Derivative

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.

Calculating Derivatives of Trigonometric Functions

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.

Calculating Derivatives of Polynomial Equations

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.

Calculating Derivatives of Exponential Equations

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.

Using the Chain Rule to Differentiate Complex Functions

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.

Differentiating Factored Polynomials: Product Rule and Expansion

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.

When to Use the Quotient Rule for Differentiation

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.

Understanding Higher Order Derivatives Using Graphs

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.

Calculating Higher Order Derivatives

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.

How to Calculate Derivatives of Inverse Trigonometric Functions

11. 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.

Applying the Rules of Differentiation to Calculate Derivatives

12. 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.

Related Rates: The Draining Tank Problem

13. Related Rates: The Draining Tank Problem

Grab an empty cup and pour some water into it. In this lesson we will watch how the height of the water changes as we learn about related rates of change and learn how to solve the draining tank problem.

Related Rates: The Distance Between Moving Points Problem

14. Related Rates: The Distance Between Moving Points Problem

Remember the classic problem of math horror stories everywhere? You know, where one train leaves Kentucky at 2 p.m. and another leaves Sacramento at 4 p. m.? In this lesson, tame the horror and learn how to solve these problems using differentiation and related rates.

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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Other Chapters

Other chapters within the FTCE Mathematics 6-12 (026): Practice & Study Guide course

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