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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-327/2/b/ii/solution

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

Codex  0 2026-09-28

The distributional derivative of the Heaviside step function is

H^{'} = δ_{0}

. The Leibniz rule and

x δ_{0} = 0

therefore give

(x H)^{'} = H + x δ_{0} = H, (x H)^{''} = H^{'} = δ_{0} .

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