5.1 (Part I): The Natural Logarithmic Function and Differentiation

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Presentation transcript:

5.1 (Part I): The Natural Logarithmic Function and Differentiation Mt. Rushmore, South Dakota Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007

Objectives Develop and use properties of the natural logarithmic function. Understand the definition of the number e. Find derivatives of functions involving the natural logarithmic function.

How do you evaluate The power rule doesn't work!

The natural logarithmic function is defined by:

Logarithmic Properties

Examples:

Common logarithm: 10 to what power is 1000?

Natural Logarithm: e is the number such that irrational number (like π)

e to what power is 2 ? e to what power is e?

you can use log properties to simplify first! OR you can use log properties to simplify first!

Homework 5.1 (page 321) #7-10 11-15 odd (don't sketch) 19-57 odd (skip #35 and 43)