Leibniz's rule is a kind of extension of this rule to partial differentiation, and, if a version of the integral other than the Riemann one is used, this theorem can be stated under a hypothesis relaxed somewhat from continuity.
Isaac Barrow outlined a geometric proof of this lemma in 1669, though it lacked a completely rigorous basis for several hundred years until proof of the generalized mean value theorem. Leibniz's rule is a kind of extension of this rule to partial differentiation, and, if a version of the integral other than the Riemann one is used, this theorem can be stated under a hypothesis relaxed somewhat from continuity. For ten points, name the theorem that was discovered by Newton and Leibniz around 1670 and that states, essentially, that differentiation and integration are inverse operations.
Isaac Barrow outlined a geometric proof of this lemma in 1669, though it lacked a completely rigorous basis for several hundred years until proof of the generalized mean value theorem.
{f}undamental {t}heorem of {c}alculus