Remark
Tag 06US, permanent. Cite it as [Bourbaki, Tag 06US].
Algebra, chapter V, § 16. Differential criteria of separability
— 1) Later (V, p. 131, Cor. 3 and p. 135, Cor. 2) we shall prove a converse to Cor. 1 of Prop. 4.
2) Every algebraic extension of a prime field is separable (V, p. 37, Cor.). Since every derivation of a prime field is zero, every derivation of an algebraic extension of a prime field is zero (Prop. 4).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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