David was a pupil of Louis Spohr and Moritz Hauptmann from 1823 to 1824 and in 1826 became a violinist at Königstädtischen Theater in Berlin.
[2] In 1843 David became the first professor of violin (Violinlehrer) at the newly founded Leipziger Konservatorium für Musik.
David worked closely with Mendelssohn, providing technical advice during the preparation of the latter's Violin Concerto in E minor.
He died suddenly in 1873, aged 63, while on a mountain excursion with his children, near Klosters in the Graubünden (Grisons) area of Switzerland.
The Chaconne in G minor attributed to Tomaso Antonio Vitali was published for the first time from a manuscript in the Sächsische Landesbibliothek in Dresden in David's well renowned violin-method Die Hohe Schule des Violinspiels (1867).
He also wrote an often-used version of the cadenza for Beethoven's violin concerto, used by 12-year old Joseph Joachim at the revival concert of this piece in 1844, under Mendelssohn.