Quote of the Day: 
"We make a living by what we get, but we make a life 
      by what we give." -- Winston Churchill

Objectives:
   The student will prove the product rule for derivatives.
   The student will apply the product rule to 
	differentiation problems.
                  
1. Bellringer.

2. To introduce the Product Rule:
	First, list rules for differentiation that we have 
		already proven:
	(A) Definition of the derivative
	(B) Derivative of a constant
	(C) Power Rule
	(D) Derivative of a sum or difference

  	Recall some of the rules the student has already 
		learned:
	(A) The limit of a sum is the sum of the limits.
	(B) The limit of a product is the product of the 
		limits.
	(C) The derivative of a sum is the sum of the 
		derivatives.
	(D) The derivative of a difference is the difference
		 of the derivatives.

	So, many calculus students conjecture that the 
		derivative of a product is the product of the 
		derivatives.  Have the students test this 
		conjecture with a few examples:

3. Example #1

 
 4. Testing the conjecture on Example #2:

5. Proof of the PRODUCT RULE

6. Extended Product Rule:
    (f g h)' = f' g h + f g' h + f g h'
    (f g h j)' =  

7. Example:   
      Given y = (5x2 - 3) (7x3 + x),  Find y'
        Answer: y' = 175x4 - 48x2 - 3    

8. Assignment: 
      p. 203 (1, 3, 5, 9, 19a, 21a,b, 33)

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