Catalyzes the formation of a Delta9 double bond, acting on saturated fatty acyl subtrates like palmitoyl-CoA (hexadecanoyl-CoA) and stearoyl-CoA (octadecanoyl-CoA) with higher desaturation activity on octadecanoyl-CoA than hexadecanoyl-CoA. 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 + octadecanoyl-CoA = (9Z)-octadecenoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O 2 Fe(II)-[cytochrome b5] + 2 H(+) + hexadecanoyl-CoA + O2 = (9Z)-hexadecenoyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O Expected to bind 2 Fe(2+) ions per subunit. The histidine box domains may contain the active site and/or be involved in metal ion binding. Belongs to the fatty acid desaturase type 1 family.