Overview
An important application of implicit differentiation is to finding the derivatives of inverse functions. Here we find a formula for the derivative of an inverse, then apply it to get the derivatives of inverse trigonometric functions.
Lecture Video and Notes
Video Excerpts
» Clip 1: Derivative of the Inverse of a Function (00:07:00)
From Lecture 5 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Derivative of the Inverse of a Function
> Download from iTunes U (MP4 - 108MB)
> Download from Internet Archive (MP4 - 108MB)
» Clip 2: Derivative of the Arctan Function (00:11:00)
From Lecture 5 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: Derivative of the Arctan Function
> Download from iTunes U (MP4 - 108MB)
> Download from Internet Archive (MP4 - 108MB)
Recitation Video
Graphing the Arctan Function
Lecture Video and Notes
Video Excerpts
» Clip 1: Derivative of the Arcsin Function (00:02:00)
From Lecture 5 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Derivative of the Arcsin Function
> Download from iTunes U (MP4 - 108MB)
> Download from Internet Archive (MP4 - 108MB)
Recitation Video
Derivative of the Arccos Function
> Download from iTunes U (MP4 - 21MB)
> Download from Internet Archive (MP4 - 21MB)
Worked Example
Derivative of the Square Root Function