Ononot — A student attempts to find the derivative of the product f(x

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Derivativeseasy

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A student attempts to find the derivative of the product $f(x) = (x^2 + 1)(x - 3)$ by differentiating each factor separately and multiplying them. That is, they calculate $f'(x) = \frac{d}{dx}(x^2 + 1) \cdot \frac{d}{dx}(x - 3)$ . Why is this approach incorrect?