Example 2

Tag 083H, permanent. Cite it as [Bourbaki, Tag 083H].

Functions of a Real Variable, chapter I, § 1. FIRST DERIVATIVE

If $U = (\alpha_{ij}(x))$ is a square matrix of order $n$ , differentiable at $x_0$ and invertible at this point, then $U^{-1}$ has derivative equal to $-U^{-1} U' U^{-1}$ at $x_0$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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