1. Derivatives of Products and Quotients
Lesson 4.2

2. Quotients Rule! 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

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

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

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

7. A Memory Trick
Given
Then

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

9. 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

10. 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

11. Assignment Lesson 4.2A Page 259 Exercises 1 – 33 odd Lesson 4.2B