This tiny note was written for 75045 Dynamical Systems in 1997. I reTeXed it in 2012 just to take advantage of some progress since then. The contents are otherwise unchanged. Available in one format: pdf for a5 paper.
Note added 2019-03-19: I just found out that this formula is known as Jacobi's formula. It is described, with a proof, in Wikipedia. There, it has the more general form d det(A)=tr(adj(A)dA), where adj(A) is the adjugate of A (the transpose of the cofactor matrix, so that adj(A) = det(A)A−1, if A is invertible).
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