5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 5.1/5.2 The Natural Logarithm Differentiation and Integration Warm‐up: Solve 1. 2. 3. Intro/Warm­up 1 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 Warm‐up Answers Solve 1. 2. 3. Warm­up Answers 2 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 Learning Targets 5.1 1. Review logarithmic rules and graph 2. Find derivatives involving logarithms 5.2 1. Integrate rational functions using logs 2. Integrate trig functions Learning Target 3 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫ Review Logarithms Properties: Graphs: I.Logs 4 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫ Logarithms New! The definition of a logarithm! Why is ln(.5) negative? Also, note: I.Logs 5 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫∫ The Derivative of Logarithms chain rule and 1. Differentiate two ways. 2. Differentiate II.The Derivative of Logarithms 6 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫∫∫ Using Logarithms to Differentiate 3. Differentiate III.Using Logarithms to Differentiate 7 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫ Integrating Logarithms 4. 5. 6. I.Integrating Logarithms 8 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫ Integrating Logarithms 7. hint: long division 8. hint: u‐substitution did this one on the board... I.Integrating Logarithms 9 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫∫ Integrals of the Six Basic Trig Functions II.Integrals of the Six Basic Trig Functions 10 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 ∫∫∫ Solving Differential Equations What does that mean? III.Solving Differential Equations 11 5.1 and 5.2 The Natural Logarithm Differentiation and Integration.notebook January 03, 2017 Your Homework AB Calculus 5.1 p.331 #6,10,14,25,30,33,39‐42,45,50,57‐75(x3), 80,86,95,102,113 AB Calculus 5.2 p.340 #6‐42(x3),55,67,70,73,77,93,97,108 BC Calculus: same as AB Homework 12.