Implicit differentiation

Below we have a plot of the Folium of Descartes, the curve defined by

x³ + y³ = 3xy

By implicit differentation, we found that

dy/dx = (y - x²)/(y² - x).

Consider the point (x, y), which is on the Folium.

Below, we have a plot of the Folium, the point we've considered, and the tangent line. You can move the point anywhere on the loop by dragging it below.

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