1. The Product & Quotient Rules
Lesson: ____
Section: 3.3
The Product & Quotient Rules
Intro to  Notation: f is a small change in the value of f. so
𝑓 ′ 𝑥 = lim ℎ→0 ∆𝑓 ℎ
∆𝑓=𝑓 𝑥+ℎ −𝑓(𝑥)
The Product Rule
Ex. 𝑑 𝑑𝑥 ( 𝑥 2 𝑒 𝑥 )
If u = f(x) and v = g(x)
are differentiable, then
𝑓𝑔 ′ = 𝑓 ′ 𝑔+𝑓𝑔′ or
Ex. 𝑑 𝑑𝑥 ( 3𝑥 2 +5𝑥) 𝑒 𝑥
𝑑(𝑢𝑣) 𝑑𝑥 = 𝑑𝑢 𝑑𝑥 ∙𝑣+𝑢∙ 𝑑𝑣 𝑑𝑥

2. The Quotient Rule 𝑑 𝑑𝑥 𝑢 𝑣 = 𝑑𝑢 𝑑𝑥 ∙𝑣−𝑢∙ 𝑑𝑣 𝑑𝑥 𝑣 2
If u = f(x) and v = g(x)
are differentiable, then
The Quotient Rule
𝑑 𝑑𝑥 𝑢 𝑣 = 𝑑𝑢 𝑑𝑥 ∙𝑣−𝑢∙ 𝑑𝑣 𝑑𝑥 𝑣 2
𝑓 𝑔 ′ = 𝑓 ′ 𝑔−𝑓𝑔′ 𝑔 2 or
Ex. 𝑑 𝑑𝑥 5 𝑥 2 𝑥 3 +1
Derivation from product rule on p.123
“DHigh Low minus High DLow over Low squared”
Stay neat & organized!
Use ( ) and [ ] to help.
Ask yourself
“is this a quotient?”
“Is this a power?”
“Is this a product?”
“Is this an exponential?”
“Is it in scoring position?”

3. Derivation of the Product Rule (p. 121)

4. Add an ex. Like the book problems with graphs of 2 functions and q’s about the deriv of the product or quotient