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In the process of rounding up the product and quotient rule, I got confused when my textbook said that the product rule should not be used if one of the factors of the product is a constant, and the quotient rule should not be used if the denominator is a single term. I've used the rules for both of these conditions and i got the answers right, the only thing was that it took longer to solve, so the question is can I still use the product and quotient rule under such conditions?

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    $\begingroup$ Sure. The rules make perfect sense in those contexts, they are just unnecessarily complicated. $\endgroup$
    – lulu
    Feb 19, 2019 at 20:54
  • $\begingroup$ @lulu; thanks I got really confused when my textbook said so. $\endgroup$
    – Taofeek
    Feb 19, 2019 at 20:56
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    $\begingroup$ Yeah these rules will work in these situations, it's just overkill. For instance, if $f(x)=c$ is a constant, then $$(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)=f(x)g'(x)=cg'(x)$$ since $f'(x)=0$. $\endgroup$
    – Dave
    Feb 19, 2019 at 21:01
  • $\begingroup$ Has your question been answered? If yes, you should accept an answer. $\endgroup$ Jun 24, 2019 at 15:05

2 Answers 2

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You can use the product/quotient rules whenever both functions are differentiable, but there are easier methods in some cases. But you will always get the correct result when you apply the product/quotient rules properly.

Note that a constant is just a special case of a differentiable function.

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When on of the term is a constant, it is equivalent to using linearity to factor out the constant. Therefore, it is unnecessary use of product and quotient rule, but not false.

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