Derivatives of Exponential Functions Lesson 4.4

An Interesting Function Consider the function y = a x Let a = 2 Graph the function and it's derivative 2 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) = e x Conclusion: 3

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

Derivative of a x Now to deal with the right hand side of the expression Try graphing Look familiar? 5

Derivative of a x Conclusion When y = a g(x) Use chain rule Similarly for y = e g(x) 6

Practice Try taking the derivatives of the following exponential functions 7

Assignments Lesson 4.4 Page 279 Exercises 1 – 61 EOO 8