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ClearAll[f] f[x0_, y0_] := D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}] /. {x -> x0, y -> y0} f[0.3, 0.5] // MatrixForm I would caution you against using MatrixForm in the definition, as that would leave you with results that cannot be easily used in further computation.


You can write something like f[{r_, θ_}] := Module[{M = D[{Sqrt[x^2 + y^2], ArcTan[x, y]}, {{x, y}}]}, Block[{x = r Cos[θ], y = r Sin[θ]}, M]] I wouldn't be surprised if this has a slightly simpler formulation. The symbolic result agrees with what I expect: Assuming[r > 0, Simplify[f[{r, θ}]]] (* {{Cos[θ], Sin[θ]}, {-(Sin[θ]/r), Cos[θ]/r}} *) ...

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