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Elementary Calculus

In today's calculus lecture, we will explore the differentiation of logarithmic and exponential functions, focusing on Section 4.3. Topics include the derivative of ln(x) and the chain rule for logarithmic functions, as well as the exponential function and its derivatives. We will also work through several examples and questions to solidify your understanding. Additionally, important announcements regarding Supplemental Instruction sessions, upcoming quizzes, and deadlines will be discussed. Don't forget to keep up with your homework, and have a great week ahead!

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Elementary Calculus

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  1. Elementary Calculus Lecture 8

  2. Today’s Agenda • Supplemental Instruction – SI Mike Filer mjfiler@eagle.fgcu.edu M 2:00 – 3:00 LIB #436 T 12:30 – 1:30 LIB #434 R 6:30 – 7:30 LIB #434 F 1:00 – 2:00 LIB #436 • Section 4.3 – Differentiation of Logarithmic and Exponential Functions • Section 4.4 – DELETE!

  3. Section 4.3 - Logarithms The Derivative of lnx The Chain Rule for Logarithmic Functions

  4. Example #1 • Differentiate

  5. Example #2 • Differentiate

  6. QUESTION #1 • Differentiate

  7. Section 4.3 – Exponentials The Derivative of the Exponential Function The Chain Rule for Exponential Functions

  8. Example #3 • Differentiate

  9. Example #4 • Differentiate

  10. QUESTION #2 • Differentiate

  11. More Examples!

  12. Example #5 • Differentiate

  13. Example #6 • Find an equation for the tangent line to

  14. QUESTION #3 • Differentiate

  15. QUESTION #4 • Find an equation for the tangent line to

  16. Section 4.3 – Growth and Decay If , then and changes at the percentage rate 100k.

  17. Example #7 • Money is deposited in a bank offering interest at an annual rate of 6% compounded continuously. Find the percentage rate of change of the balance with respect to time. Percentage Rate of Change=

  18. EXIT SURVEY • What could be done to improve the lecture portion of this class?

  19. Reminders! • Keep up with your homework on MathZone. • Quiz #6 will be next week in lab. • The last day to drop without academic penalty is this Friday, October 27. • The Final Exam is Wednesday, December 13 at 10:30am in this room!

  20. Have a Great Week!

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