Adam Clarke on Psalms 44:26

Arise for our help - Show forth thy power in delivering us from the hands of our enemies.

Redeem us - Ransom us from our thraldom.

For thy mercies' sake - למען חסדך lemaan chasdecha, On account of thy mercy. That we may have that proper view of thy mercy which we should have, and that we may magnify it as we ought to do, redeem us. The Vulgate has, Redime nos, propter nomen tuum, "Redeem us on account of thy name;" which the old Psalter thus paraphrases: "Help us in ryghtwysness, and by us (buy), that es, delyver us, that we be withouten drede; and al this for thi name Jehsu; noght for oure merite."