from The Century Dictionary and Cyclopedia
- n. A sermon or exposition of a scriptural or Talmudic theme in the synagogue on Sabbath or festival mornings. One who delivers the discourse is called darshan, that is, a preacher.
Sorry, no etymologies found.
Rabbi Mitchell Wohlberg of Beth Tfiloh in Baltimore managed to do this in his Rosh Hashanah derashah, which is now spreading virally across the internet.
Midrash continues to denote the exegetical activity of derashah, but also what can be deduced from the Biblical exposition, as well as everything that accrued around a specific Biblical book, whether aggadic (= non-legal) or halakhic (which are known, respectively, as midrashei aggadah and midrashei halakhah).