A not uncommon calculus mistake is to believe that the prod- uct rule for derivatives says that
Question:
A not uncommon calculus mistake is to believe that the prod- uct rule for derivatives says that (ƒg)' = ƒ'g'. If ƒ(x) = ex²,
determine, with proof, whether there exists an open interval
(a, b) and a nonzero function g defined on (a, b) such that
this wrong product rule is true for x in (a, b).
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