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Consider the Maclaurin series for \(\sin(x)\):$$ \sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \dots $$By differentiating both sides of this equation, find the Maclaurin series for the function \(f(x) = \cos(x)\).
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