Given f(x) = g(x)/h(x), where g′(x) and h′(x) both exist and h(x) ≠ 0, prove the quotient rule by demonstrating

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f'(x) = h(x) g'(x) g(x) h'(x) Starting with f(x) = g(x)/h(x) and solving for g(x), [h(x)] g(x) = f(x) h(x)