1. 5.1 (Part II): The Natural Logarithmic Function and Differentiation
Mt. Rushmore, South Dakota
Greg Kelly, Hanford High School, Richland, Washington
Photo by Vickie Kelly, 2007

2. 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.

3. Sometimes you can use logarithms to help differentiate non-logarithmic functions.

4. Take ln of both sides of the equation.
Differentiate of both sides of the equation.

5. You can ignore the absolute value signs!
Proof:

7. Find the relative extreme of
int c
f '(c)
(-∞,-1) -2 -
(-1,∞) +

8. Homework
5.1 (page 331)
# 65 – 77 odd,
83,
87 – 93 odd,
odd