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

3.3 Product and Quotient RuleFri Sept 25

Do Now

Evaluate each

1)

2)

3)

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:

Product Rule

• Thm- Suppose that f(x) and g(x) are differentiable at x. Then:

• Ex: f(x) = x e^x

Ex 1

• Use the product rule to find

Ex 2

• Find f’(x) if

Ex 3

• Find the derivative of the function

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.

Ex 1

• Find the derivative of

Ex 2

• Find the derivative of

Ex 3

• Find the tangent line to the graph of f(x) at x = 1

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:

Closure

• Find the derivative of each:

• HW: p.147 #1 9 15 19 27 31 39 41

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

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