1. Logarithmic Differentiation
AP Calculus AB
October 31-November 1, 2016
Mrs. Agnew

2. Essential Question Essential Vocabulary
How can you use the Laws of Logarithms to help find derivatives?
Essential Vocabulary
Logarithm
Natural Logarithm
Laws of Logarithms
Logarithmic Differentiation

3. Derivatives of Power Functions
We can find the derivative of power functions using the substitution .
Prove:
Notice that the differentiation rule for power functions is NOT the power rule!

4. Derivatives of Logarithms
An important consequence of the rule for power functions is the differentiation rules for logarithms:
Stewart Practice: page 233 #20, & page #2 – 16 (E)

5. Logarithmic Differentiation
Derivatives of complicated functions can be found more easily using logarithms
Logarithmic Differentiation WS
Logarithmic Differentiation
Take natural logarithm of both sides and simplify using Laws of Logarithms
Differentiate implicitly on both sides
Solve for y´

6. Practice & Homework Guided Practice – STEWART Homework
page #28 – 36 (Even)
Homework
pg 331 #49, 51, 57, 61, 63, 65, 81, 89, 101– 105
pg 368 #43, 45, 47, 53, 55, 57, 65, 67, 69