1. a x 2017 Special Derivatives e x, a x, ln (x), log a x AP Calculus

2. Derivative of - Analytically REM: Chain Rule:

3. Ex:

4. a x a x, ln (x), log a x REM: IFF Two Properties from the Definition: ALSO: IFF Two Properties from the Definition:

5. Proof: ln(x)

6. ln(x) EX: EX: NOTE:

7. ln(x) EX: Find the second derivative.

8. Proof: a x

9. axax Ex:

10. Proof: log a (x)

11. log a (x)

12. Live Love Learn!

13. Logarithmic Differentiation REM: Properties of Logarithms Rewrite using properties of Logs.

14. Logarithmic Differentiation Set the function equal to y. Take the natural log of both sides. Take the derivative of BOTH sides - f(y) and f(x) (implicitly) Solve for dy/dx. Then resub for y.

15. Derivative : “Function raised to a Function Power”

16. Logarithmic Differentiation

17. Last Update 10/20/10 Assignment: p. 178 # 1 – 31 odd 43, 45