i-adjective
Describes emotions, urges, or impulses that are difficult or impossible to suppress.
彼は抑えがたい怒りに震えた。
He trembled with uncontrollable anger.
その子は抑えがたい好奇心から、箱を開けてしまった。
The child opened the box out of irrepressible curiosity.
The verb meaning 'to suppress' or 'to control'; 抑えがたい is its negative potential form used as an adjective.
An auxiliary adjective meaning 'difficult to do'; attached to the masu-stem of verbs. 抑えがたい is a common lexicalized example.
Compound of the masu-stem of 抑える (おさえる, 'to suppress') + the auxiliary adjective がたい ('difficult to').