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gave the statement that derivations of smooth functions are vector fields a dedicated entry of its own, in order to be able to convieniently point to it
Taking after this style of entry, I decided to write epimorphisms of groups are surjective. Added a little on splittings of exact sequences to split idempotent, and to derivation (mentioning the notion of a derivation of a group valued in a module over that group, a la group cohomology, as a special case of derivations valued in bimodules).
I have expanded the Idea-section and typed up a detailed proof at derivations of smooth functions are vector fields.
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