Just as there are times when the erroneous version of the product rule holds there are times
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Just as there are times when the erroneous version of the product rule holds there are times when the erroneous version of the quotient rule holds. Calculate [ƒ(x)g(x)]′ and ƒ′(x)g′(x) for ƒ(x) = aek2x/(k-1) and g(x) = bekx for k ≠ 1, and verify that they are equal.
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