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

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?”

Derivation of the Product Rule (p. 121)

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