MathDB

A not uncommon calculus mistake is to believe that the product rule for derivatives says that

(fg)' = f'g'

. If

f(x)=e^{x^2}

, 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

(a,b)

Problem Statement