Unit 7: Implicit differentiation and related rates
About this unit
To differentiate an equation in x and y, differentiate both sides with y treated as a function of x, so each y-term gains a dy/dx; with time as the variable this links related rates.
By the end, you can: Find slopes on curves given by an equation in x and y by differentiating both sides, and use the same move to link rates that change together in time.
Modules
5 modulesLearn
- When y isn't on its ownArticle · Curves like x² + 4y² = 8 aren't y = f(x), but they still have slopes; differentiate both sides, and d/dx(y²) = 2y·dy/dx by the chain rule.Not started
- The slope of an ellipseWalkthrough · Find dy/dx on x² + 4y² = 8 and evaluate it at (2, 1) to get −1/2.Not started
- A spreading oil slickWalkthrough · Differentiate A = πr² with respect to time to turn a radius rate of 0.5 m/min into an area rate at r = 20 m.Not started
- The one moveReview · Differentiate both sides, attach dy/dx (or d/dt) to every term in the dependent quantity, then solve and substitute.Not started