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

Select the first clip below to begin.

» Clip 1: Other Bases (1 min)
» Accompanying Notes (PDF)

From Lecture 6 of 18.01 Single Variable Calculus, Fall 2006

» Clip 2: Derivative of a^x; Logarithmic
Differentiation (5 min)
» Accompanying Notes (PDF)

From Lecture 6 of 18.01 Single Variable Calculus, Fall 2006

» Clip 3: Derivative of x^x (3 min)
» Accompanying Notes (PDF)

From Lecture 6 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Recitation Video

Rules of Logs

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Download this video:
» iTunes U (MP4 - 20MB)
» Internet Archive (MP4 - 20MB)

Lecture Video and Notes

Video Excerpts

Select the first clip below to begin.

» Clip 1: The Power Rule (4 min)
» Accompanying Notes (PDF)

From Lecture 7 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

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