Logarithmic Differentiation

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

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

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!

Derivatives of Logarithms An important consequence of the rule for power functions is the differentiation rules for logarithms: Stewart Practice: page 233 #20, 25 & page 250 #2 – 16 (E)

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´

Practice & Homework Guided Practice – STEWART Homework page 251 #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