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Derivativeseasy
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A student attempts to find the derivative of the product f(x)=(x2+1)(x−3)f(x) = (x^2 + 1)(x - 3)f(x)=(x2+1)(x−3) by differentiating each factor separately and multiplying them. That is, they calculate f′(x)=ddx(x2+1)⋅ddx(x−3)f'(x) = \frac{d}{dx}(x^2 + 1) \cdot \frac{d}{dx}(x - 3)f′(x)=dxd​(x2+1)⋅dxd​(x−3). Why is this approach incorrect?