5 · IB Maths AA
Implicit differentiation
Choose a curve defined by an equation in x and y, drag a point along it and see dy/dx found by implicit differentiation, together with the tangent line at that point.
Drag the red point, or click the graph and use ← → (hold Shift for bigger steps).
Try this
- Circle with r = 3: drag the point to (3, 0). Watch the denominator y reach 0 — the tangent becomes vertical and dy/dx is undefined.
- Folium with a = 2 (x³ + y³ = 6xy): find where the tangent is horizontal. Check that the numerator 2y − x² is 0 there (near x ≈ 2.52, y ≈ 3.17).
- Folium again: move to (3, 3) and confirm dy/dx = −1, then slide towards the origin, where numerator and denominator are both 0.
Common error: when differentiating a term like 6xy you must use the product rule, giving 6y + 6x·(dy/dx); then collect every dy/dx term on one side and factorise before dividing.