The Freshman's Product Rule (f⋅g)' = f'⋅g' is true only if f/f' + g/g' = 1pic.twitter.com/6eHFtV7BwI
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What if f and g are both constant functions, e.g.?
Then from the first equality we see that we will have 0=0, so it will "work".
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But f' = g' =0, so your condition can't be written as it is.
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Right, so perhaps I should have said any "non constant" function.
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