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
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