Find (dy)/(dx) if x³ + y³ = 3axy.

Differentiate both sides with respect to $x$: $3x^2 + 3y^2\frac{dy}{dx} = 3a\left(y + x\frac{dy}{dx}\right)$ $x^2 + y^2\frac{dy}{dx} = ay + ax\frac{dy}{dx}$ $(y^2 - ax)\frac{dy}{dx} = ay - x^2$