9231 P11 - Nov 2011 - Q3 - 7 marks
6546
Prove by mathematical induction that, for all positive integers \(n\),
\(\frac{\mathrm{d}^{n}}{\mathrm{~d} x^{n}}\left(\mathrm{e}^{x} \sin x\right)=2^{\frac{1}{2} n} \mathrm{e}^{x} \sin \left(x+\frac{1}{4} n \pi\right) .\)
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