Unit 6

Exponential and Logarithmic Functions

Lesson 4: Derivatives of Logarithmic Functions

In Lesson 3, logarithmic functions were reviewed and the natural logarithm was introduced. Take a look at the graph of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«msub»«mi»log«/mi»«mn»2«/mn»«/msub»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mstyle»«/math» shown below. Use the graph to sketch the graph of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»y«/mi»«mo»=«/mo»«mi»f«/mi»«mo mathvariant=¨italic¨»`«/mo»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mi mathvariant=¨normal¨»)«/mi»«/mrow»«/mstyle»«/math». What kind of function results for the derivative of a logarithmic function?