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'

"xy' + y" is not "xy' + y" -- Where the heck does the x' go?x'