AP Calculus BC Monday, 21 September 2015 OBJECTIVES TSW find (1) derivatives using the product and quotient rules, and (2) higher-order derivatives. ASSIGNMENT DUE (wire basket) –Sec. 3.3: pp (7-17 odd, all omit 21, 35, 36) TODAY’S ASSIGNMENT (due W/Th, 09/23-24/15) –Sec. 3.4: pp (7, 8, 11, 12, odd, 20, 25, 26, ) –Sec. 3.3: p. 161 (44, 45, 47)

Week of 09/21/15 – 09/25/15 MONDAYSec. 3.4: Product & Quotient Rules Sec. 3.3: Higher-Order Derivatives TUESDAYSec. 3.7: The Chain Rule WED/THURSec. 3.8: Implicit Differentiation FRIDAYSec. 3.8: continued QUIZ: Product, Quotient, & Chain Rules M, 09/28/15Review: Derivatives Tu, 09/29/15TEST: Derivatives

Product and Quotient Rules and Higher-Order Derivatives

The Product Rule (first)  (derivative of the second) + (second)  (derivative of the first)

Product and Quotient Rules and Higher-Order Derivatives Ex: Find the derivative.

Product and Quotient Rules and Higher-Order Derivatives Ex: Find the derivative.

Product and Quotient Rules and Higher-Order Derivatives Ex: Find the derivative.

Product and Quotient Rules and Higher-Order Derivatives The Quotient Rule

Product and Quotient Rules and Higher-Order Derivatives Example: Find the derivative. Do NOT square the denominator

Product and Quotient Rules and Higher-Order Derivatives Ex: Find the derivative. First, eliminate the complex fraction. Now find the derivative

Product and Quotient Rules and Higher-Order Derivatives When not to use the Quotient Rule:

Product and Quotient Rules and Higher-Order Derivatives Derivatives of Trigonometric Functions Memorize MemoriZE MemorizE MemorIZE MemoRIZE MemORIZE MeMORIZE MEMORIZE

Product and Quotient Rules and Higher-Order Derivatives Higher-Order Derivatives First Derivative: n th Derivative:Fourth Derivative:Third Derivative:Second Derivative: