ATingRwith a derivation δ is called δ-semiprime if for any δ-idealIofR(i.e., an idealIsuch that δ(I)⊆I)I2= 0 impliesI= 0.Ris called δ-quasi-Baer (resp. quasi-Baer) if the right annihilator of every δ-ideal (resp. ideal) ofRis generated by an idempotent ofR. In this paper, a differential polynomial ringA = R[x;δ] of a ringRwith a derivation δ is investigated as follows: For a δ-semiprime ringR, (1)Ris δ-quasi-Baer iffAis quasi-Baer iffAis-quasi-Baer for every extended derivationonAof δ (2)Ris δ-quasi-Baer iffAis CS-module over a ringA⊗zAop.