# Ch 7: Calculating Derivatives and Derivative Rules: Tutoring Solution

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- Begin your assignment or other calculus work.
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This chapter of our calculus tutoring solution will benefit any student who is trying to learn about calculating derivatives and derivative rules and earn better grades. This resource can help students including those who:

- Struggle with understanding how to use limits, calculate derivatives of trigonometric functions, use the chain rule or quotient rule, find derivatives of implicit functions or any other derivative calculations and rules topic.
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## Learning Objectives

- Calculate derivatives using limits.
- List the linear properties of derivatives.
- Calculate derivatives of trigonometric functions, polynomial equations and exponential equations.
- Differentiate complex functions using the chain rule.
- Use the product rule and expansion to differentiate factored polynomials.
- Learn when to apply the quotient rule for differentiation.
- Use graphs to understand higher order derivatives.
- Calculate higher order derivatives.
- Calculate the derivatives of implicit functions.
- Find the derivatives of inverse trigonometric functions.
- Calculate derivatives using the rules of differentiation.

### 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.

### 14. Indefinite Integral: Definition, Rules & Examples

In this lesson, you will learn about the indefinite integral, which is really just the reverse of the derivative. We will discuss the definition, some rules and techniques for finding indefinite integrals, as well as a few examples.

### 15. Ordered Pair: Definition & Examples

An ordered pair is a simple way of keeping track of two numbers by writing them in a specific order. Learn about ordered pairs and how they are useful.

### 16. Origin in Math: Definition & Overview

The origin is more than just the (0,0) point on a graph. It is the starting point from which all other points are measured. Read this lesson to learn about how the origin is used in mathematics.

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### Other Chapters

Other chapters within the Calculus: Tutoring Solution course

- Graphing and Functions: Tutoring Solution
- Continuity: Tutoring Solution
- Geometry and Trigonometry in Calculus: Tutoring Solution
- Using Scientific Calculators in Calculus: Tutoring Solution
- Limits: Tutoring Solution
- Rate of Change: Tutoring Solution
- Graphing Derivatives and L'Hopital's Rule: Tutoring Solution
- Applications of Derivatives: Tutoring Solution
- Area Under the Curve and Integrals: Tutoring Solution
- Integration and Integration Techniques: Tutoring Solution
- Integration Applications: Tutoring Solution
- Differential Equations: Tutoring Solution