Book example (and everywhere else online):
Differentiate the folium of descartes:
x^3 + y^3 = 6xy
Left side: 3x^2 + 3y^2 y'
Right side using product rule: 6xy' + 6y
Where did the x' go? (Ignoring the 6 for now):
The product rule is (fg)' = fg' + gf'
or:
(xy)' = xy' + yx'...