Corollary

Tag 0834, permanent. Cite it as [Bourbaki, Tag 0834].

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

If $\varphi$ is a continuous linear form on $E$ , then the real function $\varphi \circ f$ has a derivative equal to $\varphi(f'(x_0))$ at the point $x_0$ .

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

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