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3 $begingroup$ This question already has an answer here: Computing second partial derivative with polar coordinates 1 answer Similar questions have been asked on this site but none of them seemed to help me. I'm asked to compute the Laplacian $$frac{partial^2}{partial x^2}+frac{partial^2}{partial y^2}$$ in terms of polar coordinates. I did do it, but I don't understand why what I did is correct, and I don't understand the more "brute force" way to do it at all. Here is what I did: I calculated $frac{partial}{partial r}$ and $frac{partial}{partial theta}$ in terms of $r,$ $theta,$ $frac{partial}{partial x}$ and $frac{partial}{partial y}.$ This gave me a system of linear equati