Chapter 6: Inverse Functions

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Course

MATH162 (Calculus II)

Overview

This chapter covers Inverse Functions from Stewart Calculus 9th Edition.

Each section contains:

Sections

Section 6.1: Inverse Functions and Their Derivatives

Skill Description Difficulty
Derivative of Inverse Functions Inverse Functions Intermediate
Finding Inverse Functions Algebraically Inverse Functions Intermediate
Graphing Inverse Functions Inverse Functions Intermediate
Inverse Function Definition Inverse Functions Beginner
Inverse Functions: Overview Inverse Functions Beginner
One-to-One Functions Inverse Functions Beginner

Section 6.2: Exponential Functions and Their Derivatives

Skill Description Difficulty
Derivatives of Exponential Functions Inverse Functions Intermediate
Derivatives of Exponential Functions (Introduction) Inverse Functions Beginner
Exponential Functions and Properties Inverse Functions Beginner
Integrals of Exponential Functions Inverse Functions Intermediate
The Number e Inverse Functions Intermediate

Section 6.3: Logarithmic Functions

Skill Description Difficulty
Laws of Logarithms Inverse Functions Intermediate
Logarithmic Functions Inverse Functions Foundational
The Natural Logarithm Inverse Functions Intermediate

Section 6.4: Derivatives of Logarithmic Functions

Skill Description Difficulty
Derivative of General Logarithms Differentiation Rules Intermediate
Derivative of the Natural Logarithm Differentiation Rules Intermediate
Integrals Yielding Natural Logarithm Integration Techniques Intermediate
Logarithmic Differentiation Differentiation Techniques Advanced
The Number e as a Limit Limits and Continuity Intermediate

Section 6.5: Exponential Growth and Decay

Skill Description Difficulty
Continuously Compounded Interest Differential Equations Intermediate
Exponential Growth and Decay Model Exponential Growth and Decay Intermediate
Exponential Growth and Decay: The ODE Model Differential Equations Beginner
Exponential Population Growth Differential Equations Intermediate
Half-Life and Radioactive Decay Differential Equations Intermediate
Newton’s Law of Cooling Differential Equations Intermediate

Section 6.6: Inverse Trigonometric Functions

Skill Description Difficulty
Derivatives of Inverse Trigonometric Functions Differentiation Rules Intermediate
Integrals Yielding Inverse Trigonometric Functions Inverse Functions Intermediate
Inverse Trigonometric Functions: Definitions and Exact Values Inverse Functions Beginner
Simplifying Expressions with Inverse Trig Functions Inverse Functions Intermediate

Section 6.7: Hyperbolic Functions

Skill Description Difficulty
Derivatives of Hyperbolic Functions Hyperbolic Functions Intermediate
Hyperbolic Function Definitions Hyperbolic Functions Beginner
Hyperbolic Identities Hyperbolic Functions Intermediate
Inverse Hyperbolic Functions Hyperbolic Functions Advanced

Section 6.8: Indeterminate Forms and l’Hospital’s Rule

Skill Description Difficulty
Converting Indeterminate Products and Differences Indeterminate Forms and L’Hospital’s Rule Intermediate
Indeterminate Differences (∞-∞) Indeterminate Forms and L’Hospital’s Rule Intermediate
Indeterminate Powers Indeterminate Forms and L’Hospital’s Rule Intermediate
L’Hospital’s Rule Limits Intermediate
L’Hospital’s Rule for Indeterminate Powers Limits Advanced
L’Hospital’s Rule for Products and Differences Limits Intermediate
L’Hospital’s Rule for Quotients Limits Intermediate
Recognizing Indeterminate Forms Limits and L’Hospital’s Rule Beginner

Prerequisites

Before starting Chapter 6, review relevant prerequisite skills from earlier chapters.

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