Implicit Differentiation of $x^3+y^3=3xy$

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Recently I came across a problem that asked to solve for the derivative of the following equation: $$x^3+y^3=3xy$$

I started by differentiating both sides, and I got $3x^2+3y^2\frac{dy}{dx}$ on the left side. But I cannot figure out out to differentiate $3xy$, because they're being multiplied together. Any help on how to complete the solution and solve for $\frac{dy}{dx}$?

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As @Andrei commented, you want to use the product rule: $$\frac{d}{dx}[xy]=\frac{d}{dx}[x]y+x\frac{d}{dx}[y]=1.y+x.\frac{dy}{dx}=y+x\frac{dy}{dx}$$ see product rule and this video is quite helpful