From Adam Clarke’s commentary of Psalm 2:7...
This day have I begotten thee - By thy resurrection thou art declared to be the Son of God, εν δυναμει, by miraculous power, being raised from the dead. Thus by thy wondrous and supernatural nativity, most extraordinary death, and miraculous resurrection, thou art declared to be the Son of God. And as in that Son dwelt all the fullness of the Godhead bodily, all the sufferings and the death of that human nature were stamped with an infinitely meritorious efficacy. We have St. Paul's authority for applying to the resurrection of our Lord these words, "Thou art my Son; this day have I begotten thee;" - see Acts 13:33; see also Hebrews 5:6; - and the man must indeed be a bold interpreter of the Scriptures who would give a different gloss to that of the apostle. It is well known that the words, "Thou art my Son; this day have I begotten thee," have been produced by many as a proof of the eternal generation of the Son of God. On the subject itself I have already given my opinion in my note on Luke 1:35, from which I recede not one hair's breadth. Still however it is necessary to spend a few moments on the clause before us. The word היום haiyom, Today, Is in no part of the sacred writings used to express eternity, or any thing in reference to it; nor can it have any such signification. To-day is an absolute designation of the present, and equally excludes time past and time future; and never can, by any figure, or allowable latitude of construction, be applied to express eternity. But why then does the Divine Spirit use the word begotten in reference to the declaration of the inauguration of the Messiah to his kingdom, and his being seated at the right hand of God? Plainly to show both to Jews and Gentiles that this Man of sorrows, this Outcast from society, this Person who was prosecuted as a blasphemer of God, and crucified as an enemy to the public peace and a traitor to the government, is no less than that eternal Word, who was in the beginning with God, who was God, and in whom dwelt all the fullness of the Godhead bodily: that this rejected Person was he for whom in the fullness of time a body was prepared, begotten by the exclusive power of the Most High in the womb of an unspotted virgin, which body he gave unto death as a sin-offering for the redemption of the world; and having raised it from death, declared it to be that miraculously-begotten Son of God, and now gave farther proof of this by raising the God-man to his right hand.
The word ילדתי yalidti, "I have begotten," is here taken in the sense of manifesting, exhibiting, or declaring; and to this sense of it St. Paul ( Romans 1:3, Romans 1:4) evidently alludes when speaking of "Jesus Christ, who was made of the seed of David according to the flesh, του ὁρισθεντος Υἱου Θεου εν δυναμει, κατα Πνευμα αγιωσυνης, εξ αναστασεως νεκρων ; and declared (exhibited or determined) to be the Son of God with power, according to the Spirit of holiness." This very rejected Person, I this day, by raising him from the dead, and placing him at my right hand, giving to him all power in heaven and earth, declare to be my Son, the beloved one in whom I am well pleased. Therefore hear him, believe on him, and obey him; for there is no redemption but through his blood; no salvation but in his name; no resurrection unto eternal life but through his resurrection, ascension, and powerful intercession at my right hand. Thou art my Son; this day have I declared and manifested thee to be such. It was absolutely necessary to the salvation of men, and the credibility of the Gospel, that the supernatural origin of the humanity of Jesus Christ should be manifested and demonstrated. Hence we find the inspired writers taking pains to show that he was born of a woman, and of that woman by the sovereign power of the everlasting God. This vindicated the character of the blessed virgin, showed the human nature of Christ to be immaculate, and that, even in respect to this nature, he was every way qualified to be a proper atoning sacrifice and Mediator between God and man. I need not tell the learned reader that the Hebrew verb ילד yalad, to beget, is frequently used in reference to inanimate things, to signify their production, or the exhibition of the things produced. In Genesis 2:4; : These are the generations, תולדות toledoth, of the heavens and the earth; this is the order in which God produced and exhibited them. See Hebrews and Eng. Concord., Venema, etc.