Most of these meanings appear somewhere in the Tanach (with the exception of "preach, lecture"). So we can't claim biblical usage as a sign of original meaning.
Klein actually provides an etymology:
JAram.-Syr. דרש, Mand. דרש (= he examines; he instructed, taught). Arabic darasa (= he learned, studied), Ethiopian darasa (= he expounded, interpreted) are Aramaic loan words. The original meaning of this base probably is 'to tread, trample, rub', hence ultimately identical with base דרס.
Klein defines דרס as "to tread, trample" but doesn't explain the connection to darash there either. Perhaps one of you can see the connection between דרס and דרש, but nothing seems obvious to me.
Stahl, in his Arabic dictionary, connects דרש to both דרס and also to דוש, which means "to tread, thresh" (possibly based on Gesenius here). He writes (my translation):
studying requires repetition, as does the threshing of grain
He points us to the word "studio" for similar development. From the Online Etymology Dictionary for the word "study":
c.1125, from O.Fr. estudier "to study" (Fr. étude), from M.L. studiare, from L. studium "study, application," originally "eagerness," from studere "to be diligent" ("to be pressing forward"), from PIE *(s)teu- "to push, stick, knock, beat"
The problem with this theory is that darash only appears once in the Tanach with the meaning "to study" - in Ezra 7:10. This seems to be a pretty late source, and none of the dictionaries put that meaning near the top. Heschel, in Heavenly Torah: As Refracted through the Generations, (pages 251-252) describes the shift of meaning in Ezra's time:
Scripture says that Ezra "dedicated himself to seek out the meaning [lidrosh] of the Torah of the Lord" (Ezra 7:10)
and in footnote 45, there continues:
It is worth noting that this verse expresses something of historic importance. Previously, the root drsh was used for seeking out God, that is, for consulting an oracle, a priest or a prophet. Now it is used for the teaching of God, for the Torah. Ezra begins to inquire of a test, and thus we are signaled that the era of prophecy is at an end.The Encyclopedia Judaica article on "Midrash" (found here), also points to the Latin studium, but has a somewhat different description than Stahl:
The term Midrash itself derives from the root drsh (דרש) which in the Bible means mainly “to search,” “to seek,” “to examine,” and “to investigate” (cf. Lev. 10:16; Deut. 13:15; Isa. 55:6; et al.). This meaning is also found in rabbinic Hebrew (cf. BM 2:7: “until thou examine [tidrosh] thy brother if he be a cheat or not”). The noun “Midrash” occurs only twice in the Bible (II Chron. 13:22 and 24:27); it is translated in the Septuagint by βίβλοs, γράφη i.e., “book” or “writing,” and it seems probable that it means “an account,” “the result of inquiry (examination, study, or search) of the events of the times,” i.e., what is today called “history” (the word history is also derived from the Greek root ίστορὲω which has a similar meaning). In Jewish literature of the Second Temple period the word Midrash was first employed in the sense of education and learning generally (Ecclus. 51:23), “Turn unto me, ye unlearned, and lodge in my house of Midrash,” which the author’s grandson translated into Greek, “house of instruction or of study”; compare the similar development of the Latin studium which originated in the verb studeo which means “to become enthusiastic,” “to make an effort,” “to be diligent,” etc. and only in a secondary sense, in the post-Augustan era, in the sense of learning (with diligence and the noun studium passed through the same stages of meaning; cf. Ger. studium; Fr. étude, etc.).
So if I understand Moshe David Herr's EJ article, he says that first the word darash meant "to search" or "to seek", and from there developed to the sense of "to study", with a similar pattern in Latin. However, that leaves an obvious question. Where would the connection to דרס fit in to Herr's theory?
In the Theological Dictionary of the Old Testament, Wagner has an extensive discussion about the usage and meaning of the root דרש, on pages 293-307. In the section on etymology, he writes:
The root drs is found in several Semitic languages: Aramaic, Arabic, Ethiopic, Syriac and Mandean, and is attested in Ugaritic (as yet only once, according to Bauer's reconstruction). It is debatable whether Akkadian darasu has anything to do with the same root. The original meaning of drs is hard to determine. It is probably correct to translate it by the English words "seek," "ask," "inquire (of)" (Ugar. "interrogate, question"?). The root must have undergone a change of meaning in the course of its use. In late Semitic languages such as Middle Hebrew, Jewish Aramaic and Syriac one encounters meanings like "interpret," but also "tread," "trample".
So Wagner basically reverses Klein's theory and says that דרס followed דרש.
Gesenius supports Klein, by saying that the original meaning was "to tread a place, i.e. to go or come to it, to frequent" and from there "to seek, to search for". I'm not sure who's right. Gesenius is the only one to flush out Klein's theory (of course Klein read Gesenius, not the other way around), but it seems somewhat forced. And the fact that darash never actually means "to tread" in Biblical Hebrew leads me to give more weight to Wagner's theory.
Regardless of the original meaning, by Talmudic times the verb darash came to be almost exclusively associated with study, meaning "to expound, interpret" or "to teach, lecture". The former sense gave us the word מדרש midrash (actually appearing once in the Tanach - Divrei Hayamim II 13:22) meaning "homelitical interpretation", and the latter sense we find in both the words derasha דרשה - "sermon" and beit midrash בית מדרש - "house of study".
This Philologos column discusses the connection between the Hebrew beit midrash and the Arabic madrasah - "school":
Madraseh, like many terms used by the world's Muslims, comes from Arabic, in which it is a nominal form of the verb darasa, "to study." In contemporary Arabic, however, madrasa does not necessarily mean a religious seminary. It is the generic word for "school," so that a second-grader learning to read and write is attending a madrasa, too. It is only in non-Arabic languages spoken by Islamic peoples that the word specifically refers today to a religious institution of higher learning.In Modern Hebrew, as often happens, we've returned to the Biblical sense, and the most common usage of דרש is "to require".
As for the Jewish beit midrash, or "house of study," it comes from the verb darash, "to seek" (exactly as the talib of "Taliban" comes from talaba, "to seek"), and goes back to early rabbinic times in Palestine — that is, to the very beginning of the Common Era. Jewish education in this period began with a beit sefer, a "house of the book" (the generic Hebrew word for "school" to this day) in which young children were taught reading, writing and Bible; continued with a beit talmud, or "house of learning," in which some Mishna and simple rabbinic jurisprudence was taught to older children, and progressed to a beit midrash, in which advanced students sat at the feet of famous rabbis. The original beit midrash was thus similar to what eventually came to be known among Jews as a yeshiva, literally, "a sitting." Over the centuries, however, as the word yeshiva replaced beit midrash for an institute of higher Jewish learning, beit midrash came to denote an informal place of study in which anyone could sit and learn on his own in the presence of a library of sacred books.
The interesting question is whether the linguistic connection between the Muslim madrasa and the Jewish beit midrash is more than a matter of the general kinship between Arabic and Hebrew and actually has a causal element — i.e., whether the word madrasa was modeled on beit midrash. Although I can't think of any way of proving or disproving this, my instincts tell me that it was probably what happened. Rabbinic Judaism had an enormous influence on early Islam, and many Islamic institutions and concepts were knowingly or unknowingly taken from it. Moreover, when one reflects that pre-Islamic Arab society had no system of formal education at all; that the word kuttab is allied to kitab, "book," like sefer in beit sefer, and that the original beit midrash was an institution of higher religious learning just as the madrasa was, it seems likely that early Islam borrowed its terminology for different kinds and stages of schooling at least partly from Jewish sources.
In the spirit of seeking and studying, I'd like to ask (not demand!) from my readers some help. In the course of researching this post, I found this page. In the section discussing Sanskrit, they write:
Among the derivative verbal systems are the causative and the desiderative ("desire to"); the former has an affix -ay- (gam-ay-a-ti "makes to go," kar-ay-a-ti "has do") or, after roots in -a, -pay- (stha-pay-a-ti "sets in place"). The desiderative is formed with -sa- and reduplication (repetition of a part of the root)--di-drk-sa-te "desires to see" (root drsh). The desiderative also has an agent noun in -u--di-drk-s-u "who wishes to see."Does anyone know if there's a suggested connection between the Sanskrit and the Hebrew drsh? Let's keep the suggestions in the realm of peshat, not derash...
Update: I've given the question of darash / daras some more thought, and I think I overlooked something. In addition to daras, we have another verb that clearly means "tread" - דרך darach. Klein says that darach is related to דרג - also meaning "to walk". So now we have three roots that mean "to tread/ walk", which leads me to believe that perhaps we're talking about an early two-letter Hebrew root. We might also be able to add דדב - "to be accustomed, be trained" and דרר - "to flow abundantly, run swiftly". In that case, it's not so farfetched to think that darash is also connected, maybe similar to Gesenius. First "to walk", then "to seek".