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Let \(f : \mathbb{R} \to \mathbb{C}\), \(f(t) = \exp(i \alpha t)\) for a fixed \(\alpha \in \mathbb{R}\). Compute \(f'(t)\), then \(f^{(n)}(t)\) for every \(n \in \mathbb{N}\). (Admit \((\cos)' = -\sin\) and \((\sin)' = \cos\) from Standard functions.)
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