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when you differentiate for example 1/x are the top terms of the quotient rule inter changable?

Mathematics
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No, it has to be (the derivative of the top times the bottom) minus (the top times the derivative of the bottom).
I always just used the product rule. Never bothered with the quotient rule. You can rewrite the quotient rule as the product rule and deal with stuff that way. I think it's conceptually easier to do and easier to derive if you forget where it comes from.
ok got it. thank you very much for clearing that up

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