Session 15: Implicit Differentiation and Inverse Functions

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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

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» Clip 1: Derivative of the Inverse of a Function (00:07:00)

» Accompanying Notes (PDF)

From Lecture 5 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Derivative of the Arctan Function (00:11:00)

» Accompanying Notes (PDF)

From Lecture 5 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

Graphing the Arctan Function

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Lecture Video and Notes

Video Excerpts

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» Clip 1: Derivative of the Arcsin Function (00:02:00)

» Accompanying Notes (PDF)

From Lecture 5 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

Derivative of the Arccos Function

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Worked Example

Derivative of the Square Root Function

 

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