1. Exponential and Log Derivatives
AP Calculus Unit 3 Day 7
Exponential and Log Derivatives

2. ARRIVAL PRACTICE
Continued

3. ARRIVAL PRACTICE

6. g is continuous and differentiable at x = 0
More PRACTICE
g is continuous and differentiable at x = 0
g is continuous, but not differentiable at x = 0
g is not continuous, but is differentiable at x = 0
g is not continuous or differentiable at x = 0
Nothing can be said about differentiability at x = 0

7. 4. The position, in feet, of a particle can be described by
More PRACTICE
4. The position, in feet, of a particle can be described by
the function: Find the velocity of
the particle at t = 2 seconds.
(Calculator active)

8. Today’s topic: Exponential Derivatives

9. Exponential Rules
Easiest derivative!

10. Think about the implications for
The slope of the tangent line at any point on is equal to the y -value at that point.
(1,0)

12. Exponential Rules (PINK SHEET)
Easiest derivative!
Exponential functions with a base other than “e”.
Note: “a” is a number!
Using the chain rule (exponent is more than just an “x”)

13. Examples:
Find the derivative:

14. Examples:
Find the derivative:

15. Logarithmic Derivatives

16. Logarithmic Rules (PINK SHEET)
Basic natural log derivative
Log functions with a base other than “e”.
Note: “a” is a number!
Using the chain rule (inner function is more than just an “x”)

17. Examples:
Find the derivative: