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 with a = 3 a = 2.5 a = 2.7

3. An Interesting Function
Consider that there might be a function that is its own derivative
Try f (x) = ex
Conclusion:
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4. 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?
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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) Similarly for y = eg(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