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

### About This Chapter

## 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

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### Other Chapters

Other chapters within the TExES Physics/Mathematics 7-12 (243): Practice & Study Guide course

- TExES Physics/Math 7-12: Teaching Math & Science
- TExES Physics/Math 7-12: Basic Arithmetic
- TExES Physics/Math 7-12: Real Numbers
- TExES Physics/Math 7-12: Decimals & Fractions
- TExES Physics/Math 7-12: Ratios, Percent & Proportions
- TExES Physics/Math 7-12: Exponents & Exponential Expressions
- TExES Physics/Math 7-12: Algebraic Expressions & Equations
- TExES Physics/Math 7-12: Rational Expressions
- TExES Physics/Math 7-12: Radical Expressions
- TExES Physics/Math 7-12: Complex & Imaginary Numbers
- TExES Physics/Math 7-12: Number Theory
- TExES Physics/Math 7-12: Vector Operations
- TExES Physics/Math 7-12: Sequences & Series
- TExES Physics/Math 7-12: Functions
- TExES Physics/Math 7-12: Graphing & Functions
- TExES Physics/Math 7-12: Linear Equations
- TExES Physics/Math 7-12: Quadratic Equations
- TExES Physics/Math 7-12: Graphing & Factoring Quadratic Equations
- TExES Physics/Math 7-12: Matrices & Determinants
- TExES Physics/Math 7-12: Polynomials
- TExES Physics/Math 7-12: Exponential & Logarithmic Functions
- TExES Physics/Math 7-12: Trigonometry
- TExES Physics/Math 7-12: Continuity in Calculus
- TExES Physics/Math 7-12: Limits in Calculus
- TExES Physics/Math 7-12: Foundations of Geometry
- TExES Physics/Math 7-12: Geometry and Measurement
- TExES Physics/Math 7-12: Geometric Figures
- TExES Physics/Math 7-12: Parallel Lines & Polygons
- TExES Physics/Math 7-12: Properties of Triangles
- TExES Physics/Math 7-12: Geometric Solids
- TExES Physics/Math 7-12: Analytical Geometry
- TExES Physics/Math 7-12: Similar Polygons
- TExES Physics/Math 7-12: Conic Sections
- TExES Physics/Math 7-12: Circular Arcs & Circles
- TExES Physics/Math 7-12: Triangle Theorems & Proofs
- TExES Physics/Math 7-12: Statistics
- TExES Physics/Math 7-12: Probability
- TExES Physics/Math 7-12: Discrete Probability Distributions
- TExES Physics/Math 7-12: Continuous Probability Distributions
- TExES Physics/Math 7-12: Statistical Inference
- TExES Physics/Math 7-12: Mathematical Reasoning
- TExES Physics/Math 7-12: Applied Math
- TExES Physics/Math 7-12: Scientific Inquiry & Process
- TExES Physics/Math 7-12: Vectors & Scalars
- TExES Physics/Math 7-12: Kinematics
- TExES Physics/Math 7-12: Motion
- TExES Physics/Math 7-12: Fluid Mechanics
- TExES Physics/Math 7-12: Linear Momentum
- TExES Physics/Math 7-12: Work, Energy & Power
- TExES Physics/Math 7-12: Laws of Gravitation
- TExES Physics/Math 7-12: Oscillations
- TExES Physics/Math 7-12: Rotational Motion & Conservation of Energy
- TExES Physics/Math 7-12: Heat & Energy
- TExES Physics/Math 7-12: Thermodynamics
- TExES Physics/Math 7-12: Electrical Forces & Fields
- TExES Physics/Math 7-12: Potential & Capacitance
- TExES Physics/Math 7-12: Current Circuits
- TExES Physics/Math 7-12: Magnetism
- TExES Physics/Math 7-12: Waves, Sound & Light
- TExES Physics/Math 7-12: Quantum Physics
- TExES Physics/Mathematics 7-12 Flashcards