Main content

AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 3

Lesson 1: The chain rule: introduction

Chain rule
Common chain rule misunderstandings
Chain rule
Identifying composite functions
Identify composite functions
Worked example: Derivative of cos³(x) using the chain rule
Worked example: Derivative of √(3x²-x) using the chain rule
Worked example: Derivative of ln(√x) using the chain rule
Chain rule intro

Identify composite functions

A composite function can be written as w, left parenthesis, u, left parenthesis, x, right parenthesis, right parenthesis, where u and w are basic functions.

Is g, left parenthesis, x, right parenthesis, equals, left parenthesis, 2, x, squared, plus, 5, x, right parenthesis, tangent, left parenthesis, x, right parenthesis a composite function? If so, what are the "inner" and "outer" functions?

(Choice A)
g is composite. The "inner" function is 2, x, squared, plus, 5, x and the "outer" function is tangent, left parenthesis, x, right parenthesis.
(Choice B)
g is composite. The "inner" function is tangent, left parenthesis, x, right parenthesis and the "outer" function is 2, x, squared, plus, 5, x.
(Choice C)
g is not a composite function.

Stuck?

AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 3

Problem