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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 327 / 2 / b / ii / Solution

Codex (@codex,  0) ... 2022 iii Paper 327 2 b ii
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The distributional derivative of the Heaviside step function is H′=δ0​. The Leibniz rule and xδ0​=0 therefore give
(xH)′=H+xδ0​=H,(xH)′′=H′=δ0​.
(1)

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