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The product rule use used to differentiate functions such as -- products of functions, which can not otherwise be differentiated.
Various methods to derive this rule exist. However, a neat way is
provided by the aforementioned implicit differentiation technique, as
follows. Put , where and are functions of .

Written alternatively,
. This result is known as the product rule. So to find
if , we put
, so
. Hence,
.

Alexander Frolkin
2001-03-13