# Ch 27: TExMaT Master Mathematics Teacher 8-12: Rules for Calculating Derivatives

### About This Chapter

## TExMaT Master Mathematics Teacher 8-12: Rules for Calculating Derivatives - Chapter Summary

Get ready for TExMaT Master Mathematics Teacher 8-12 exam questions requiring you to differentiate complex functions, such as trig functions and factored polynomials. Video lessons in this chapter cover the following differential calculus topics:

- Uses of limits to calculate derivatives
- Linear properties of derivatives
- Applications of the product rule
- Uses of the chain rule
- Tips for applying the quotient rule

Whether you need an in-depth review of the steps involved in differentiating functions or just want a quick refresher on a particular derivative rule, these videos and transcripts enable you to work through chapter material at your own pace. You'll also find multiple-choice quizzes that link back to video content, allowing you to identify areas that could use some extra study time or affirm your understanding of these calculus concepts before moving on to the next chapter.

### TExMaT Master Mathematics Teacher 8-12: Rules for Calculating Derivatives Chapter Objectives

Responses to the multiple-choice and constructed-response questions appearing on this TExMaT exam are used to assess the preparedness of applicants for Texas's Master Mathematics Teacher certification in grades 8-12. Precalculus and calculus concepts make up around 16% of exam content. Calculus questions designed to measure your understanding of derivative properties and your ability to use differentiation techniques are the focus of this chapter's test-prep resources.

### 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. 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.

### 4. 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.

### 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.

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### Other Chapters

Other chapters within the TExMaT Master Mathematics Teacher 8-12 (089): Practice & Study Guide course

- TExMaT Master Mathematics Teacher 8-12: Properties of Real Numbers
- TExMaT Master Mathematics Teacher 8-12: Fractions
- TExMaT Master Mathematics Teacher 8-12: Decimals & Percents
- TExMaT Master Mathematics Teacher 8-12: Ratios & Proportions
- TExMaT Master Mathematics Teacher 8-12: Measurements & Conversions
- TExMaT Master Mathematics Teacher 8-12: Reasoning & Problem Solving
- TExMaT Master Mathematics Teacher 8-12: Vector Operations
- TExMaT Master Mathematics Teacher 8-12: Matrices & Determinants
- TExMaT Master Mathematics Teacher 8-12: Exponents & Exponential Expressions
- TExMaT Master Mathematics Teacher 8-12: Algebraic Expressions
- TExMaT Master Mathematics Teacher 8-12: Linear Equations
- TExMaT Master Mathematics Teacher 8-12: Inequalities
- TExMaT Master Mathematics Teacher 8-12: Absolute Value Problems
- TExMaT Master Mathematics Teacher 8-12: Quadratic Equations
- TExMaT Master Mathematics Teacher 8-12: Polynomials
- TExMaT Master Mathematics Teacher 8-12: Rational Expressions
- TExMaT Master Mathematics Teacher 8-12: Radical Expressions
- TExMaT Master Mathematics Teacher 8-12: Systems of Equations
- TExMaT Master Mathematics Teacher 8-12: Complex Numbers
- TExMaT Master Mathematics Teacher 8-12: Functions
- TExMaT Master Mathematics Teacher 8-12: Piecewise Functions
- TExMaT Master Mathematics Teacher 8-12: Parametric Equations
- TExMaT Master Mathematics Teacher 8-12: Exponential & Logarithmic Functions
- TExMaT Master Mathematics Teacher 8-12: Continuity of Functions
- TExMaT Master Mathematics Teacher 8-12: Limits
- TExMaT Master Mathematics Teacher 8-12: Rate of Change
- TExMaT Master Mathematics Teacher 8-12: Graphing Derivatives
- TExMaT Master Mathematics Teacher 8-12: Applications of Derivatives
- TExMaT Master Mathematics Teacher 8-12: Area Under the Curve & Integrals
- TExMaT Master Mathematics Teacher 8-12: Integration Techniques
- TExMaT Master Mathematics Teacher 8-12: Integration Applications
- TExMaT Master Mathematics Teacher 8-12: Foundations of Geometry
- TExMaT Master Mathematics Teacher 8-12: Geometric Figures
- TExMaT Master Mathematics Teacher 8-12: Properties of Triangles
- TExMaT Master Mathematics Teacher 8-12: Triangle Theorems & Proofs
- TExMaT Master Mathematics Teacher 8-12: Parallel Lines & Polygons
- TExMaT Master Mathematics Teacher 8-12: Quadrilaterals
- TExMaT Master Mathematics Teacher 8-12: Circular Arcs & Circles
- TExMaT Master Mathematics Teacher 8-12: Conic Sections
- TExMaT Master Mathematics Teacher 8-12: Geometric Solids
- TExMaT Master Mathematics Teacher 8-12: Analytical Geometry
- TExMaT Master Mathematics Teacher 8-12: Trigonometric Functions
- TExMaT Master Mathematics Teacher 8-12: Trigonometric Graphs
- TExMaT Master Mathematics Teacher 8-12: Solving Trigonometric Equations
- TExMaT Master Mathematics Teacher 8-12: Trigonometric Identities
- TExMaT Master Mathematics Teacher 8-12: Sequences & Series
- TExMaT Master Mathematics Teacher 8-12: Data & Statistics
- TExMaT Master Mathematics Teacher 8-12: Summarizing Data
- TExMaT Master Mathematics Teacher 8-12: Tables & Plots
- TExMaT Master Mathematics Teacher 8-12: Probability
- TExMaT Master Mathematics Teacher 8-12: Discrete Probability Distributions
- TExMaT Master Mathematics Teacher 8-12: Continuous Probability Distributions
- TExMaT Master Mathematics Teacher 8-12: Sampling
- TExMaT Master Mathematics Teacher 8-12: Hypothesis Testing
- TExMaT Master Mathematics Teacher 8-12: Regression & Correlation
- TExMaT Master Mathematics Teacher 8-12 Flashcards