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