How to find stationary points of two-variable cubic

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I need to differentiate this cubic function to get the stationary points: $$f(x,y) = x^3 + ax^2 + bxy^2 + cxy + dx + e,$$ where $a$, $b$, $c$, $d$ and $e$ are constants.

How do I do this?

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HINT: solve the system $$d+2ax+3x^2+cy+by^2=0$$ $$cx+2bxy=0$$