# Use of the product and quotient rule in differentiation

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?

• Sure. The rules make perfect sense in those contexts, they are just unnecessarily complicated.
– lulu
Feb 19, 2019 at 20:54
• @lulu; thanks I got really confused when my textbook said so. Feb 19, 2019 at 20:56
• 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 $f'(x)=0$.
– Dave
Feb 19, 2019 at 21:01
• Has your question been answered? If yes, you should accept an answer. Jun 24, 2019 at 15:05

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.

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.