# Ch 46: CEOE Advanced Math: Derivative Calculations & Rules

### About This Chapter

## CEOE Advanced Math: Derivative Calculations & Rules - Chapter Summary

Use this chapter to explore derivative calculations and rules as you plan to ace the CEOE Advanced Math examination. Engaging video lessons comprise the chapter. They're designed to help you review familiar math concepts or learn new ones. When you complete your studies, you might be capable of:

- Calculating derivatives and their linear properties as well as derivatives of trigonometric functions
- Understanding higher order derivatives using graphs
- Higher order derivatives
- Derivatives of implicit functions and inverse trigonometric functions
- Using the rules of differentiation

Knowledgeable instructors walk your through each concept and are available to answer any questions you may have. Short, engaging video lessons are accompanied by transcripts and self-assessment quizzes. Use the jump feature under the Timeline tab to go directly to main subjects within the video.

### Derivative Calculations & Rules - Chapter Objectives

The CEOE Advanced Mathematics exam measures a student's knowledge of subject matter in accordance with Oklahoma educator licensure regulations. The exam measures mathematical processes and number sense; relations functions, and algebra; measurement and geometry; trigonometry and calculus; and probability, statistics, and discrete mathematics. The material covered in this Derivative Calculations and Rules chapter is tested in the trigonometry and calculus portion of the CEOE exam, which comprises about 23% of the entire test. The exam includes approximately 80 multiple-choice questions and one open-response question.

### 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.

### 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. 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.

### 4. 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.

### 5. 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.

### 6. How to Find Derivatives of Implicit Functions

How do you define the rate of change when your function has variables that cannot be separated? Learn how implicit differentiation can be used to find dy/dx even when you don't have y=f(x)!

### 7. 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.

### 8. 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.

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### Other Chapters

Other chapters within the OSAT Advanced Mathematics (CEOE) (111): Practice & Study Guide course

- CEOE Advanced Math: Mathematical Reasoning & Ideas
- CEOE Advanced Math: Origins of Math
- CEOE Advanced Math: Absolute Value
- CEOE Advanced Math: Inequalities
- CEOE Advanced Math: Integers
- CEOE Advanced Math: Operations with Fractions
- CEOE Advanced Math: Operations with Decimals
- CEOE Advanced Math: Percents
- CEOE Advanced Math: Rational & Irrational Numbers
- CEOE Advanced Math: Complex Numbers
- CEOE Advanced Math: Properties of Numbers
- CEOE Advanced Math: Exponents & Exponential Expressions
- CEOE Advanced Math: Roots & Radical Expressions
- CEOE Advanced Math: Number Theory
- CEOE Advanced Math: Vectors, Matrices & Determinants
- CEOE Advanced Math: Properties of Functions
- CEOE Advanced Math: Graphing Functions
- CEOE Advanced Math: The Coordinate Graph & Graph Symmetry
- CEOE Advanced Math: Linear Equations
- CEOE Advanced Math: Systems of Linear Equations
- CEOE Advanced Math: Quadratic Functions
- CEOE Advanced Math: Polynomial Functions Basics
- CEOE Advanced Math: Higher-Degree Polynomial Functions
- CEOE Advanced Math: Piecewise, Absolute Value & Step Functions
- CEOE Advanced Math: Rational Expressions & Function Graphs
- CEOE Advanced Math: Exponential & Logarithmic Functions
- CEOE Advanced Math: Measurement
- CEOE Advanced Math: Perimeter & Area
- CEOE Advanced Math: Symmetry, Similarity & Congruence
- CEOE Advanced Math: Properties of Lines
- CEOE Advanced Math: Angles
- CEOE Advanced Math: Triangles
- CEOE Advanced Math: Triangle Theorems & Proofs
- CEOE Advanced Math: Similar Polygons
- CEOE Advanced Math: The Pythagorean Theorem
- CEOE Advanced Math: Circles
- CEOE Advanced Math: Circular Arcs & Measurement
- CEOE Advanced Math: Transformations
- CEOE Advanced Math: Analytic Geometry & Conic Sections
- CEOE Advanced Math: Trigonometric Functions
- CEOE Advanced Math: Trigonometric Graphs
- CEOE Advanced Math: Trigonometric Applications
- CEOE Advanced Math: Limits
- CEOE Advanced Math: Continuity
- CEOE Advanced Math: Rate of Change
- CEOE Advanced Math: Graphing & Applying Derivatives
- CEOE Advanced Math: Area Under the Curve & Integrals
- CEOE Advanced Math: Integration Techniques
- CEOE Advanced Math: Differential Equations
- CEOE Advanced Math: Data & Graphs
- CEOE Advanced Math: Samples & Populations
- CEOE Advanced Math: Probability
- CEOE Advanced Math: Sets
- CEOE Advanced Math: Statistics
- CEOE Advanced Math: Number Patterns & Sequences
- CEOE Advanced Math: Number Patterns & Series
- CEOE Advanced Math: Discrete Math
- OSAT Advanced Mathematics (CEOE) (111) Flashcards