Derivatives of Exponential Functions

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Presentation transcript:

Derivatives of Exponential Functions Lesson 4.4

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

An Interesting Function Consider that there might be a function that is its own derivative Try f (x) = ex Conclusion: View Geogebra Demo

What is the justification for each step? Derivative of ax When f(x) = ax Consider using the definition of derivative What is the justification for each step? View Geogebra Demo

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

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

Practice Try taking the derivatives of the following exponential functions

Assignments Lesson 4.4 Page 279 Exercises 1 – 61 EOO