Let $R$ be a commutative ring of characteristic zero. Under certain conditions we determine the type of derivations of a skew polynomial ring $A_n=R[X_1,X_2,\dots,X_n;d_1,d_2,\dots,d_n]$ over $R$, where $d_1,d_2,\dots,d_n$ are derivations of $R$ commuting to each other, and we examine properties of the ideals of $A_n$.