# Ch 14: Finding Derivatives

### About This Chapter

## Finding Derivatives - Chapter Summary and Learning Objectives

Differentiation is one of the most basic elements of calculus, so this chapter is stacked with lessons on calculating derivatives in trigonometric, polynomial, and complex functions. Solidify your understanding of calculating higher order derivatives and derivatives of implicit functions. Through these bite-sized videos, our expert instructors cover these topics and more, such as inverse trigonometric functions. In each lesson you will find memorable graphics to hold your attention and maximize retention and a quiz to assess your synthesis of the key points. Among the topics in this chapter you will learn to:

- Calculate derivatives of trigonometric, polynomial, and complex equations
- Use the Chain Rule
- Differentiate factored polynomials and higher-order derivatives
- Find derivatives of implicit functions, inverse trigonometric functions, and exponential equations
- Work with parametric, polar, and vector derivatives

Video | Objective |
---|---|

Calculating Derivatives of Trigonometric Functions | In this video our instructors describe how the derivatives of sin(x), cos(x), and tan(x) are cos(x), -sin(x), and sec^2(x) respectively. |

Calculating Derivatives of Polynomial Equations | Learn how to use the Power Rule to quickly find the derivative of polynomial equations. |

Using the Chain Rule to Differentiate Complex Functions | Here our instructors describe how to pick apart complex functions with layers of parentheses by differentiating from the outside to the inside. |

Differentiating Factored Polynomials: Product Rule and Expansion | In this lesson you will learn about the Product Rule and how it helps to find derivatives with functions involving multiplication. |

Understanding Higher Order Derivatives Using Graphs | This video pits cartoons against uneven functions as the instructors describe second- and higher-order derivatives in graphical form. |

Calculating Higher Order Derivatives | Instructors describe what jerks changes in acceleration are with this video on derivatives of derivatives. |

How to Find Derivatives of Implicit Functions | This lesson shows how to separate out inseparable elements of a function by taking the derivative of both sides of the equation and factoring out the derivative terms. |

How to Calculate Derivatives of Inverse Trigonometric Functions | Here you will get a few more equations to memorize as you explore inverse trigonometric functions. |

Applying the Rules of Differentiation to Calculate Derivatives | This video explores how to use the product, quotient, and chain rules in real-world examples. |

Calculating Derivatives of Exponential Equations | This video teaches you four more rules to remember when dealing with derivatives of exponentials. |

Derivatives of Functions: Parametric, Polar & Vector | We revisit parametric, polar, and vector functions in this lesson on more complex derivative cases. |

### 1. Finding Derivatives of Sums, Products, Differences & Quotients

This lesson will go over how to find the derivative of a sum, difference, product, and quotient. We will look at the different formulas involved in these derivatives and use those formulas to calculate some derivatives.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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)!

### 9. 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.

### 10. 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.

### 11. 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.

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### Other Chapters

Other chapters within the AP Calculus BC: Exam Prep course

- Graph Basics
- The Basics of Functions
- How to Graph Functions
- Limits of Functions
- Function Continuity
- Understanding Exponentials & Logarithms
- Using Exponents and Polynomials
- Parametric, Polar and Vector Functions
- Properties of Derivatives
- The Derivative at a Point
- The Derivative as a Function
- Second Derivatives
- Derivative Applications
- Properties of Definite Integrals
- Applications of Integrals
- Using the Fundamental Theorem of Calculus
- Applying Integration Techniques
- Approximation of Definite Integrals
- Understanding Sequences & Series
- Series of Constants
- Taylor Series
- Using a Scientific Calculator for Calculus
- AP Calculus BC Flashcards