Unit 5: The product and chain rules
About this unit
A product grows by each factor's change times the other factor, (fg)′ = f′g + fg′, and a function of a function changes at the outer rate times the inner rate, f′(g(x))·g′(x).
By the end, you can: See why the derivative of a product is f′g + fg′ and why rates multiply through a function inside a function, then use both rules to find slopes.
Modules
5 modulesLearn
- Products grow two ways; rates multiplyArticle · Revenue p·q changes by about p·dq + q·dp (the dp·dq corner is negligible); a temperature per km times km per minute gives temperature per minute.Not started
- A product: x sin xWalkthrough · Use (fg)′ = f′g + fg′ to find the slope of x·sin x at x = π/2, which is 1.Not started
- A chain: √(x² + 9)Walkthrough · Split √(x² + 9) into an outer square root and an inner x² + 9, multiply the rates, and get a slope of 0.8 at x = 4.Not started
- Two rules side by sideReview · Product: f′g + fg′, never f′g′. Chain: outer derivative at the inner value, times the inner derivative.Not started