Freshman product rule

WRONG WRONG WRONG
This article describes a wrong rule, that one may be tempted to believe is true.

Statement

This is a wrong rule, and it states that the derivative of the product is the product of the derivatives, i.e., that:

$\frac{d}{dx}[f(x)g(x)]=f^{\prime }(x)g^{\prime }(x)$

There is a corresponding correct rule that enables the differentiation of products. This is the product rule for differentiation.