2. 3.9: Derivatives of Exponential and Logarithmic Functions

5. Look at the graph of The slope at x=0 appears to be 1. If we assume this to be true, then: definition of derivative

6. Now we attempt to find a general formula for the derivative of using the definition. This is the slope at x=0, which we have assumed to be 1.

8. is its own derivative! If we incorporate the chain rule: We can now use this formula to find the derivative of

9. ( and are inverse functions.) (chain rule)

10. ( is a constant.) Incorporating the chain rule:

11. Example At what point on the graph of the function y = 2 t – 3 does the tangent line have slope 21?

12. Example At what point on the graph of the function y = 2 t – 3 does the tangent line have slope 21?

13. So far today we have: Now it is relatively easy to find the derivative of.

15. To find the derivative of a common log function, you could just use the change of base rule for logs: The formula for the derivative of a log of any base other than e is:

16. Example A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the value of m?

17. Example A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the value of m?

18. Example Find dy/dx if y = log a a sin x.

19. Example Find dy/dx if y = log a a sin x.

20. 

22. Example