Kähler differentials of a polynomial algebra (${\Omega }_{k[X_i]/k}={⨁}_{i}k[X_i]d{X}_i$)

The Kähler differentials of a polynomial ring are free on the differentials of its variables. Assigning arbitrary values to these generators uniquely defines a derivation. Applying the Conormal exact sequence for Kähler differentials to a quotient gives its presentation by the formal derivatives of its defining equations.