Product Rule
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High Quality Content by WIKIPEDIA articles! It is a common error, when studying calculus, to suppose that the derivative of (uv) equals (u )(v ) (Leibniz himself made this error initially); however, there are clear counterexamples to this. For a (x) whose derivative is '(x), the function can also be written as (x) · 1, since 1 is the identity element for multiplication. If the above-mentioned misconception were true, (u )(v ) would equal zero. This is true because the derivative of a constant (such as 1) is zero and the product of '(x) · 0 is also zero.

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High Quality Content by WIKIPEDIA articles! It is a common error, when studying calculus, to suppose that the derivative of (uv) equals (u )(v ) (Leibniz himself made this error initially); however, there are clear counterexamples to this. For a (x) whose derivative is '(x), the function can also be written as (x) · 1, since 1 is the identity element for multiplication. If the above-mentioned misconception were true, (u )(v ) would equal zero. This is true because the derivative of a constant (such as 1) is zero and the product of '(x) · 0 is also zero.