← MATH 01130 · Calculus I
MATH 01130 · Derivatives
Implicit differentiation
Definition
When y is defined by an equation F(x,y)=0 rather than y=f(x), differentiate both sides wrt x, treating y as y(x), then solve for dy/dx.
Read this
Every y term picks up a dy/dx (chain rule). Example: d/dx[y²]=2y y′.
Useful for circles, ellipses, and relations that are painful to solve for y.
Second derivatives: differentiate y′ again; substitute y′ from the first step to simplify.
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 3
Click the card to flip
Try this
Attempt each problem first, then open the worked solution.
1.Find dy/dx for x³ + y³ = 6xy.