Freshman product rule: Difference between revisions
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==Statement== | |||
This is a ''wrong'' rule, and it states that the derivative of the product is the product of the derivatives, i.e., that: | |||
<math>\frac{d}{dx}[f(x)g(x)] = f'(x)g'(x)</math> | |||
There is a corresponding ''correct'' rule that enables the differentiation of products. This is the [[product rule for differentiation]]. | |||
Latest revision as of 15:44, 15 October 2011
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:
![{\displaystyle {\frac {d}{dx}}[f(x)g(x)]=f'(x)g'(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0eb0a065cc536a6816090186923dc3fe93c2bbc)
There is a corresponding correct rule that enables the differentiation of products. This is the product rule for differentiation.