| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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| Session | November |
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| Topic | Proof by induction |
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3 Prove by mathematical induction that, for all positive integers \(n\),
$$\frac { \mathrm { d } ^ { n } } { \mathrm {~d} x ^ { n } } \left( \mathrm { e } ^ { x } \sin x \right) = 2 ^ { \frac { 1 } { 2 } n } \mathrm { e } ^ { x } \sin \left( x + \frac { 1 } { 4 } n \pi \right)$$