2.12 Derivatives of Exponential and Logarithm Functions

Summary

By the end of your studying, you should know:

• The derivative of e^x.
• The derivative of ln(x).
• How to write a^x in terms of e^x; and to use this formula to compute the derivative of a^x.
• How to write log to the base a of x in terms of ln(x); and to use this formula to compute the derivative of the general logarithm function.
• How to find a solution of the differential equation y' = ky.

On-screen applet instructions: For any x, the red dot represents the difference quotient for the natural log at x for a given h. Use the slider to let h → 0.

Examples Let y = ln(x2 + y2). Find y'. Let Find y'. Show that there is a point at which the derivative of the function p(x) = ex – 3x is equal to zero. Applets Limits of Functions Videos See short videos of worked problems for this section. Quiz Take a quiz. Exercises See Exercises for 2.12 Derivatives of Exponential and Logarithm Functions (PDF). Work online to solve the exercises for this section, or for any other section of the textbook.

Resources on the Web Information on Newton Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Information on Leibniz Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Calculus Applications Project Intermath Derivatives of Exponentials and Logs IES

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2.11 Implicit Differentiation

Table of Contents

2.13 Newton?s Method

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel