1. AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp. 170-171 (7, 8, 11, 12, 15-19 odd, 20, 25, 26, 40. 41) –Sec. 3.3: p. 161 (44, 45, 47) TODAY’S ASSIGNMENT (due Friday, 09/25/15) –Sec. 3.7: pp. 198-199 (7-10 all, 19-33 odd (omit 27), 57, 61, 65)

2. Sec. 3.7: The Chain Rule

3. Easy to differentiate: Not easy to differentiate: Easy to differentiate: Not easy to differentiate: Easy to differentiate: Not easy to differentiate:

4. Sec. 3.7: The Chain Rule How does one item change with respect to another? Ex: There are 3 gears, labeled #1, #2, and #3. Gear one is the smallest, followed by gear two, and finally gear three. #1 rotates four times as fast as #2. #2 rotates five times as fast as #3. How much faster is #1 rotating than #3? (4)(5) = 20 times as fast This demonstrates the CHAIN RULE.

5. Sec. 3.7: The Chain Rule The Chain Rule

6. Sec. 3.7: The Chain Rule Ex: Differentiate:

7. Sec. 3.7: The Chain Rule The General Power Rule

8. Sec. 3.7: The Chain Rule Ex: Differentiate:

9. Sec. 3.7: The Chain Rule Ex: Differentiate:

10. Sec. 3.7: The Chain Rule Ex: Differentiate:

11. Sec. 3.7: The Chain Rule Ex: Find all points on the graph of

12. Sec. 3.7: The Chain Rule Ex: Find all points on the graph of

13. Sec. 3.7: The Chain Rule Ex: Differentiate:

14. Sec. 3.7: The Chain Rule Ex: Differentiate:

15. Sec. 3.7: The Chain Rule Ex: Differentiate:

16. Sec. 3.7: The Chain Rule Ex: Differentiate:

17. Sec. 3.7: The Chain Rule Ex: Differentiate:

18. Sec. 3.7: The Chain Rule Ex: Differentiate:

19. Sec. 3.7: The Chain Rule Summary of Differentiation Rules

20. Sec. 3.7: The Chain Rule PPT Problems (put on a clean sheet of notebook paper):  Due tomorrow/Thursday, 09/23-24/15. Find each derivative; simplify your answer.