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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