Derivative of the Determinant Function

Hi there. If I were to compute the derivative of the determinant
function as a function of the linear space of n x n matrices, how would
I go about doing this? My initial thought was to treat this as a Hodge
duality problem, but I'm not really sure where to begin if I take this
approach. I was just wondering if anyone could offer me some input,
thanks.

-Corey

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