APFIVE Terms From Implicit Differentiation
Consider the implicit equation $$x^3+y^3-3*x*y=0$$ (the Folium of Descartes). Differentiating yields:
$$3*x^2+ 3*y^2*(dy/dx) - 3*(y+x*(dy/dx)) = 0.$$
When expanded, the terms appear in the order: $$3*x^2, 3*y^2*(dy/dx), -3*y, -3*x*(dy/dx).$$
Rank these terms in that left-to-right order.
| Label | Expression |
|---|---|
| A | $$3*x^2$$ |
| B | $$3*y^2*(dy/dx)$$ |
| C | $$-3*y$$ |
| D | $$-3*x*(dy/dx)$$ |
A
3x^2, -3y, 3y^2(dy/dx), -3x(dy/dx)
B
3x^2, 3y^2*(dy/dx), -3x(dy/dx), -3*y
C
3y^2(dy/dx), 3x^2, -3y, -3x(dy/dx)
D
3x^2, 3y^2*(dy/dx), -3y, -3x*(dy/dx)
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