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Exploring Derivatives of Logarithmic Functions in Calculus

Understand the derivatives of natural logarithmic functions, their properties, applications in growth and decay problems, and how to compute values using a calculator. Show formula steps and answers in full sentences with attention to units. Bonus points available!

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Exploring Derivatives of Logarithmic Functions in Calculus

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  1. MAT 1221Survey of Calculus Section 4.5 Derivatives of Logarithmic Functions http://myhome.spu.edu/lauw

  2. Expectations • Show formula steps • For problem 2 • Formally answer the question in full sentence • Pay attention to the units

  3. Bonus Point Friday!? • 2 bonus points for your next exam • Come and listen to an applied math themed presentation (probability, limits, and derivatives) • OMH 139, 5:10 – 5:50 • Fill in a survey • Limited seats, sign up sheet is going around

  4. Natural Logarithmic Functions • Log. Functions are defined as the inverse function of the exponential functions.

  5. Natural Logarithmic Functions • Log. Functions are defined as the inverse function of the exponential functions. • In particular, and

  6. Natural Logarithmic Functions • Log. Functions are defined as the inverse function of the exponential functions. • In particular, and • Bad Notation: is incorrect since ln is a function not a number

  7. Graph

  8. Other Properties (You have learned these from a previous class…)

  9. Calculator • Locate the natural log. function in your calculator. • Compute the value of

  10. Applications is widely used to solveGrowth and Decay problems in conjunction with .

  11. Formula

  12. Formula

  13. Example 1

  14. Remark (Need this later…)

  15. Example 2

  16. Example 3

  17. Example 4

  18. Expectations • If possible, simplify the functions before taking derivatives. • Simplify the answers.

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