# Ch 7: Calculating Derivatives: Calculus Lesson Plans

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### About This Chapter

## Weekly Syllabus

Below is a sample breakdown of the Calculating Derivatives chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day | Topics | Key Terms and Concepts Covered |
---|---|---|

Monday | Using Limits to Calculate the Derivative; The Linear Properties of a Derivative; Calculating Derivatives of Trigonometric Functions | Calculating constant and not-so-constant velocity; A look at constant and distributive type rules; An exploration of this process |

Tuesday | Calculating Derivatives of Polynomial Equations; Calculating Derivatives of Exponential Equations; Using the Chain Rule to Differentiate Complex Functions | The basic rules of this process; A look at derivatives of exponentials; Discovering when to use the chain rule |

Wednesday | Differentiating Factored Polynomials: Product Rule and Expansion; When to Use the Quotient Rule for Differentiation; Understanding Higher Order Derivatives Using Graphs | Two methods of differentiating; The importance of knowing when to use the quotient rule and when not to use it; A look at acceleration and the rate of change |

Thursday | Calculating Higher Order Derivatives; How to Find Derivatives of Implicit Functions | The process of calculating the third and fourth derivatives; A list of the necessary steps |

Friday | How to Calculate Derivatives of Inverse Trigonometric Functions; Applying the Rules of Differentiation to Calculate Derivatives | The basic rules for solving trigonometric problems; The most common rules for solving derivatives |

### 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. 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 11. 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)!

### 12. 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.

### 13. 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 Calculus Syllabus Resource & Lesson Plans course

- Graphing & Functions: Calculus Lesson Plans
- Continuity: Calculus Lesson Plans
- Geometry & Trigonometry: Calculus Lesson Plans
- Using Scientific Calculators: Calculus Lesson Plans
- Limits: Calculus Lesson Plans
- Rate of Change: Calculus Lesson Plans
- Derivative Graphs & L'Hopital's Rule: Calculus Lesson Plans
- Applications of Derivatives: Calculus Lesson Plans
- Area Under the Curve & Integrals: Calculus Lesson Plans
- Integration: Calculus Lesson Plans
- Integration Applications: Calculus Lesson Plans
- Differential Equations: Calculus Lesson Plans