1988 Putnam A2

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 $x$ in $(a,b)$.

一个并不罕见的微积分错误是相信乘积规则

对于衍生品来说 $(fg)' = f'g'$。如果$f(x)=e^{x^2}$，

通过证明判断是否存在开区间 $(a,b)$

以及在 $(a,b)$ 上定义的非零函数 $g$ ，这样错误

乘积规则对于 $(a,b)$ 中的 $x$ 成立。