9231 P11 - Nov 2025 - Q3 - 7 marks
5883
Prove by mathematical induction that, for every positive integer \(n\),
\(\frac{d^{2n-1}}{dx^{2n-1}}(x\cos x)=(-1)^n\left(x\sin x-(2n-1)\cos x\right).\)
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