Freshman product rule

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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'(x)g'(x)

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