From her tired expression, I deduced that she didn't sleep well last night.

deduced 是动词 deduce 的过去式。deduce 由前缀 de-（表示"向下、完全"）和词根 duce（来自拉丁语 ducere，意为"引导"）组成，字面意思是"完全引导出来"，引申为"通过推理得出结论"，即"推断、推论"。