1. SECTION 5-5A Part I: Exponentials base other than e

2. Variables in the exponent Logarithmic differentiation is used to find derivatives of exponential functions: 1) Which if these is an exponential function?

3. Definition of exponential function with base a Let a be a positive real number where a ≠1 and let x be any real number, then the exponential function to the base a is defined by: Bases other than e

4. Properties a) b) c) d)

5. Definition of logarithmic function with base a Let a be a positive real number where a ≠1 and let x be any real number, then the logarithmic function to the base a is defined by: Change of base formula

6. Properties a) b) c) d)

7. Differentiate

8. Derivatives for bases other than e Let a be a positive real number where a ≠1 and let u be a differentiable function of x such that: I. II.

9. Derivatives for bases other than e Let a be a positive real number where a ≠1 and let u be a differentiable function of x such that: III. IV. Proof pg 364

10. Differentiate

11. PRODUCT RULE Differentiate

13. Careful: not the power rule!

14. Differentiate

15. Through the magic of math:

16. Assignment Page 368 # 41-48, 51- 60, 63- 65, and 67 all