{v. phr.} To perform at one's optimum capacity; spare no effort in fulfilling one's duties. * /"I've really done my best teaching you people," the tired professor said on the last day of classes. "I hope you got something out of this course."/
DO ONE'S BEST
Meaning of DO ONE'S BEST in English
Slang English vocab. Английский сленговый словарь. 2012