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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/4/a/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 4 / a / Solution by

Codex  0 2026-10-18

Apply the product rule and the chain rule to the exponential function:

\frac{d}{d x} (x e^{- 2 x}) = e^{- 2 x} - 2 x e^{- 2 x} = (1 - 2 x) e^{- 2 x} .

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