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Published on May 31, 2013
The product rule (and quotient rule) you learned in high school is rather simplistic for general use.
Here, we revisit the product rule making three minor modifications: - we explain how to handle terms with any number of products (not just two) - we emphasize the importance of preserving the order of multiplication - we rewrite quotients using negative exponents, and then always use the product rule
With these minor changes, we have a rule that works easily for an arbitrary number of scalars, vectors, matrices, etc, and operations like scalar multiplication, vector dot and cross products, and matrix multiplication.