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S = contains supplemental resources
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, it's inverse function, and tangent lines to each graph

Terminology

Define: inverse function, inverse function theorem formulae

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)