1. Derivatives of Products and Quotients Lesson 4.2

2. Quotients Rule! 2 Products Rule! This lesson will show us how to take derivatives of products and quotients.

3. Review We know what to do with constant times a function For k f(x) We also know what to do with the sum of functions When Then 3

4. Product Rule Consider the product of two functions It can be shown (see proof, pg 215) that In words: The first function times the derivative of the second plus the second times the derivative of the first 4

5. Try It Out Given the following functions which are products Determine the derivatives 5

6. Quotient Rule When our function is the quotient of two other functions … The quotient rule specifies the derivative In words: The denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator 6

7. OK … Try That! Use the quotient rule on the following functions 7

8. Average Cost Suppose we have a function y = C(x) which gives us the cost of manufacturing x items The average cost is Then the marginal average cost is 8

9. Average Cost Suppose the cost for manufacturing x items is Write the function for the average cost What is the marginal average cost? Determine rate of change of the average cost for 5 items … for 50 items 9

10. Assignment Lesson 4.2A Page 259 Exercises 1 – 33 odd Lesson 4.2B Page 260 Exercises 39 – 49 odd 10