Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
Topic: Derivatives
Subtopic: Derivatives of Inverse Functions

Overview

In preparation for finding the derivatives of the inverse trig functions, today we study the derivative of a general inverse function. The formulae is of particular importance. Although complicated, understanding the graphical relationships between f(x), f^-1(x), and tangent lines to these curves will help make more concrete the concept of derivative in general.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.10.1 Find the derivative of an inverse function using the inverse function theorem formula: (f^-1)'(x)=1/(f'(f^-1(x)))
• 2.10.2 Find the derivative of an inverse function at a given value using the inverse function theorem formula: (f^-1)'(y)=1/(f'(x)) where y=f(x)
• 2.10.3 Understand the graphical relationships of a function, its inverse function, and tangent lines to each graph

Terminology

Terms you should be able to define: inverse function, inverse function theorem formulae

Mini-Lectures and Examples

Supplementary Resources

If you need to review functions and their inverses from a pre-calculus course before tackling their derivatives, be sure that you understand all the topics listed in my Pre-calculus Functions and Graphs Checklist. PurpleMath: Inverse Functions and The Math Page: Inverse Functions are adequate review sites if needed.

Supplemental Resources (optional)

rev. 2020-10-24