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Det[D[{(1+x y)^3 z + y^2 (1 + x y) (4 + 3x y), y + 3x (1 + x y)^2 z + 3x y^2 (4 + 3x y), 2x - 3x^2 y - x^3 z}, {{x,y,z}}]]
Det[D[{(1+x y)^3 z + y^2 (1 + x y) (4 + 3x y), y + 3x (1 + x y)^2 z + 3x y^2 (4 + 3x y), 2x - 3x^2 y - x^3 z}, {{x,y,z}}]]
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