Session 18: Derivatives of other Exponential Functions

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Overview

This session introduces the technique of logarithmic differentiation and uses it to find the derivative of a^x. Substituting different values for a yields formulas for the derivatives of several important functions. Further applications of logarithmic differentiation include verifying the formula for the derivative of x^r, where r is any real number.

Lecture Video and Notes

Video Excerpts

» Clip 1: Other Bases (00:01:00)

» Accompanying Notes (PDF)

From Lecture 6 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Derivative of ax, Logarithmic (00:05:00)

» Accompanying Notes (PDF)

From Lecture 6 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Derivative of xx (00:03:00)

» Accompanying Notes (PDF)

From Lecture 6 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

Rules of Logs

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> Download from iTunes U (MP4 - 20MB)

> Download from Internet Archive (MP4 - 20MB)

> Download English-US transcript (PDF)

> Download English-US caption (SRT)

Lecture Video and Notes

Video Excerpts

» Clip 1: The Power Rule (00:04:00)

» Accompanying Notes (PDF)

From Lecture 7 of 18.01 Single Variable Calculus, Fall 2006

 

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