Why is the derivative of the magnitude of a cross product not equivalent to the magnitude of the derivative of a cross product? It seems like both would have the same physical representation.
2026-04-03 11:48:29.1775216909
Derivatives of cross products
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The derivative of the magnitude of any vector valued function need not be the magnitude of the derivative. The magnitude of the derivative of $(x, y) $ with respect to $x$ is $1$. The derivative of the magnitude is $\frac x{\sqrt{x^2+y^2}}$.