For a matrix $L$ and $W$,
Is $\frac{d}{ds} L = LW$ implies $\frac{d}{ds} \det(L) = \det(L) tr(W)$?
Is $\frac{d}{ds} \det(L) = \det(\frac{d}{ds}L)$ true? ( I guess not)
2026-04-11 12:56:26.1775912186
Differentiation of determinant. Is $\frac{d}{ds} L = LW$ implies $\frac{d}{ds} \det(L) = \det(L) tr(W)$?
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$(\det(L))'=tr(L'adj(L))=tr(LWadj(L))=tr(adj(L)LW)=\det(L)tr(W)$.