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Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 327 / 3 / a / ii / Solution

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The Leibniz rule writes every derivative of a1​a2​ as a finite sum of products of derivatives of the two factors. Multiplying the corresponding symbol estimates adds their orders, so
a1​a2​∈Sym(X,Rk;N1​+N2​)​.
(1)

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