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Exploring Exponential Function Derivatives

Dive into the world of exponential functions and their derivatives through graphs and practice exercises. Investigate functions like y=ax and f(x)=ex to understand their derivatives. Learn the chain rule and explore functions that are their own derivatives. Use step-by-step justifications to deepen your understanding.

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Exploring Exponential Function Derivatives

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  1. Derivatives of Exponential Functions Lesson 4.4

  2. An Interesting Function • Consider the function y = ax • Let a = 2 • Graph the function and it's derivative Try the same thing witha = 3a = 2.5a = 2.7

  3. An Interesting Function • Consider that there might be a function that is its own derivative • Try f (x) = ex • Conclusion:

  4. Derivative of ax • When f(x) = ax • Consider using the definition of derivative What is the justification for each step?

  5. Derivative of ax • Now to deal with the right hand side of the expression • Try graphing • Look familiar?

  6. Derivative of ax • Conclusion • When y = ag(x) • Use chain rule • Similarly for y = eg(x)

  7. Practice • Try taking the derivatives of the following exponential functions

  8. Assignments • Lesson 4.4 • Page 279 • Exercises 1 – 61 EOO

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