9231 P13 - Nov 2024 - Q02 - 6 marks
4151
Prove by mathematical induction that, for all positive integers n,
\(\frac{d^n}{dx^n} \left( \arctan x \right) = P_n(x) (1 + x^2)^{-n},\)
where \(P_n(x)\) is a polynomial of degree \(n - 1\).
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