The adverb of synthetic: by a chemical process made by people, rather than naturally. It almost always sits in front of a past participle — 'synthetically produced', 'synthetically made', 'synthetically derived' — and it belongs to science writing, medicine, food labels and industry reports. Vitamin C in a tablet is synthetically produced; the vitamin C in an orange is not, and chemically they are the same thing, which is the point such sentences are usually making. Vanilla flavouring is the classic example: the natural pod costs a fortune, the synthetically produced version costs almost nothing, and most people cannot tell. You will not hear this word much in conversation — people say 'man-made' or 'artificial' instead — so treat it as a reading-and-writing word. It can also take the negative meaning of synthetic, describing behaviour that is put on rather than felt, but that use is rare and sounds odd; if you mean a smile is fake, say 'falsely' or 'insincerely'.