Discovery By Leibniz
Discovery of this rule is credited to Gottfried Leibniz (however, Child (2008) argues that it is due to Isaac Barrow), who demonstrated it using differentials. Here is Leibniz's argument: Let u(x) and v(x) be two differentiable functions of x. Then the differential of uv is
Since the term duยทdv is "negligible" (compared to du and dv), Leibniz concluded that
and this is indeed the differential form of the product rule. If we divide through by the differential dx, we obtain
which can also be written in "prime notation" as
Read more about this topic: Product Rule
Famous quotes containing the words discovery and/or leibniz:
“The discovery of Pennsylvania’s coal and iron was the deathblow to Allaire. The works were moved to Pennsylvania so hurriedly that for years pianos and the larger pieces of furniture stood in the deserted houses.”
—For the State of New Jersey, U.S. public relief program (1935-1943)
“Navarette, a Chinese missionary, agrees with Leibniz and says that “It is the special providence of God that the Chinese did not know what was done in Christendom; for if they did, there would be never a man among them, but would spit in our faces.””
—Matthew Tindal (1653–1733)