The following is a subquestion of a unanswered question posted two days ago by some user in math.stackexchange (answer that question if you prefer).
For a (not necessarily cocartesian) commutative square of commutative rings, $$\begin{array}{ccc} A&\rightarrow&B\\\ \downarrow&&\downarrow\\\ A'&\rightarrow&B' \end{array}$$ in EGA 0$_{IV}$20.5.4 there is a map written as $d_{B/A} \otimes 1: B' \to \Omega_{B/A} \otimes_BB'$, where $d_{B/A}: B \to \Omega_{B/A}$ is the canonical derivation. Since $d_{B/A}$ is not a $B$-module homomorphism, how is this map defined?