1. Product and Quotient Rules

2. Product Rule Many people are tempted to say that the derivative of the product is equal to the product of the derivatives (similar to addition and subtraction), but consider –What is product of derivatives? –What is derivative of products? –Are they equal?

3. Product Rule Theorem 3.4.1 If f and g are differentiable at x, then so is the product of, and In words, the derivative of a product is: The first times the derivative of the second plus the second times the derivative of the first.

4. Example 1 Find dy/dx if

5. 2) Find if

6. Quotient Rule Theorem 3.4.2 If f and g are differentiable at x and, then f/g is differentiable at x and In words the derivative of a quotient is Low d-high minus high d-low all over the denominator squared.

7. Example 3 Find for

8. Example 4 By differentiating, find the exact locations of the horizontal tangent lines. Then check by graphing.

9. Practice Page 203 1-25 odd