AP Calculus BC Tuesday, 22 September 2015 OBJECTIVE TSW apply the Chain Rule to differentiate functions. ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. 3.4: pp.

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Presentation transcript:

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

Sec. 3.7: The Chain Rule

Easy to differentiate: Not easy to differentiate: Easy to differentiate: Not easy to differentiate: Easy to differentiate: Not easy to differentiate:

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.

Sec. 3.7: The Chain Rule The Chain Rule

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule The General Power Rule

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Ex: Differentiate:

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

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

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Ex: Differentiate:

Sec. 3.7: The Chain Rule Summary of Differentiation Rules

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.