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


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.


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


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

Mini-Lectures and Examples

STUDY: Derivatives - Exponential, Logarithmic, Inverse, and Inverse Trig Functions

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)

Video: The Inverse Trigonometric Functions, Selwyn Hollis's Video Calculus

Lesson: Inverse Functions, Dale Hoffman's Contemporary Calculus

rev. 2020-10-24