。
I'll check how effective the medicine is.
Literal
Medicine [gen-の] effectiveness [obj-を] investigate-[try-てみる]-[polite-ます].
~てみる ('try doing, do and see') is a very common auxiliary that signals attempting an action experimentally — distinct from 試す ('test'). 効き目 is a native Japanese compound (効く + 目) meaning 'visible effect,' parallel to 効果 but more colloquial.