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:
Proof
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
Top Related