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Derivatives of Logarithmic Functions
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  1. Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.

  2. Review Laws of Logs • Algebraic Properties of Logarithms • Product Property • Quotient Property • Power Property • Change of base

  3. Definitions to Remember

  4. Example 1 • Find dy/dx for each of the following:

  5. Example 2 (Try) • Find

  6. Example 3 (try) • Find

  7. Example 4 • Find

  8. Example 4 • Find • We will use our rules of logs to make this a much easier problem.

  9. Example 4 • Now, we solve.

  10. Logarithmic Differentiation • This is another method that makes finding the derivative of complicated problems much easier. • Find the derivative of

  11. Logarithmic Differentiation • Find the derivative of • First, take the natural log of both sides and treat it like example 3.

  12. Logarithmic Differentiation • Find the derivative of • First, take the natural log of both sides and treat it like example 3.

  13. Logarithmic Differentiation • Find the derivative of

  14. Homework • Pages 247-248 • 1-33 odd