| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2017 |
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| Session | Specimen |
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| Topic | Proof by induction |
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3 Given that \(a\) is a constant, prove by mathematical induction that, for every positive integer \(n\),
$$\frac { \mathrm { d } ^ { n } } { \mathrm {~d} x ^ { n } } \left( x \mathrm { e } ^ { a x } \right) = n a ^ { n - 1 } \mathrm { e } ^ { a x } + a ^ { n } x \mathrm { e } ^ { a x }$$