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So I have the following homework. I don't want the answer, only point me in the right direction please. Thanks.

I'm stuck in the product rule. Do I apply the product rule twice or just one time after applying the quotient rule?

$$ \frac{(2x^7-x^2)(x-1)}{(x+1)} $$

I get this. $$ \frac{(x+1)\frac{d}{dx}(2x^7-x^2)(x-1)-(2x^7-x^2)(x-1)\frac{d}{dx}(x+1)}{(x+1)^2} $$

By writing this down here I think I answered my own question. I should apply the product rule to the first $$(2x^7-x^2)(x-1)$$ but not to the second one, since the second one (after the '-' sign) doesn't have the $$\frac{d}{dx}$$ am I right?

Sorry for any confusion.

ItsMitch
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  • I suspect you've answered your own question as you suggest. You have a quotient: the quotient rule applies. The numerator has a product. The quotient rule: $let N = numerator, D = denominator \to \frac{\mathrm d}{\mathrm dx}\big(\frac{N}{D}) = \frac{D\frac{\mathrm d}{\mathrm dx}(N) - \frac{\mathrm d}{\mathrm dx}(D)N}{D^2}$ In your case, the numerator has a product which you must take into account when running the quotient rule. – Andrew Falanga May 12 '13 at 00:25

1 Answers1

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Why not just expand the product in the numerator so that you have $$\frac{2x^{8} - x^{3} - 2x^{7} + x^{2}}{x+1}$$

Then you just apply the quotient rule, no problems.

More to the point of your question, though, I only see one application of the product rule. Apply the quotient rule, and in taking the derivative of the expression in the numerator, you use the product rule. As you said in your post, I don't see any product in the second expression to apply the product rule to, so I think you've got it.

Alex Wertheim
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