1. 3.3 Product and Quotient Rule Fri Sept 25 Do Now Evaluate each 1) 2) 3)

2. Product Rule Consider our derivative rules so far. We do not know the derivative if 2 terms are multiplied together Note: the derivative of a product is NOT the product of the derivatives:

3. Proof

4. Product Rule Thm- Suppose that f(x) and g(x) are differentiable at x. Then: Ex: f(x) = x e^x

5. Ex 1 Use the product rule to find

6. Ex 2 Find f’(x) if

7. Ex 3 Find the derivative of the function

8. Quotient Rule Thm- Suppose that f and g are differentiable at x and g(x) not equal to 0, then: This is especially useful when we cannot simplify the fraction.

9. Ex 1 Find the derivative of

10. Ex 2 Find the derivative of

11. Ex 3 Find the tangent line to the graph of f(x) at x = 1

12. Cases where the Product and Quotient rules are not needed Sometimes, it’s easier to simplify and use the power rule instead of the product or quotient rule Ex:

13. Closure Find the derivative of each: HW: p.147 #1 9 15 19 27 31 39 41