Calculus Lesson 3.1: Chain Rule

We will use the Chain Rule to find the derivative of multiple composite functions.

Content Objective #2

We will differentiate a composite function using the Chain Rule

​Content Objective #1

In Topic 2, we discovered the multiple methods that can be used to calculate derivatives.

Of course we know that functions will come in different shapes and sizes so we need to expand our derivative techniques.

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​Introduction

Take the derivative of the outside function, times the derivative of the inside function.

Process

Derivative rule used to find derivatives of composite functions. (i.e. functions inside of other functions)

Definition

Discuss: When composing functions, what do we usually replace? What is a clue that something has been replaced?

Identifying functions

Where f(x) is the outside function and g(x) is the inside function.

Given h(x)
- What is the inside function?
- What is the outside function?

Rule

Step 1: Identify the composite function. Find f and g. Label

Step 2: Find f' and g'

Step 3: Set up f' with g function inside.

Step 4: Find g'. Multiply and simplify.