find-the-derivative-of-each-function-by-using-the-quotient-rule-yfrac2-x2-x-1x2x2-2

Question

Find the derivative of each function by using the quotient rule.
$$y=\frac{2 x^{2}-x-1}{x^{2}(x+2)}$$

Gregory Higby · Accepted Answer

alright in this problem, I think they&#x27;re trying to get you to do the product rule and the quotient rule at the same time, uh which I&#x27;ll go ahead and do it that way. I probably wouldn&#x27;t if I were teaching this. So because if you notice in the denominator of this quotient, so there&#x27;s your quotient, but down here you have um you have a product. So the way I would probably do is think about in the denominator, the denominator would be equal to X to the third power plus two X squared when you distribute. Um So I guess I could do both. Thinking about it where I show you dy dx where the drift of of the top is For X -1, then you leave the bottom alone, so I&#x27;m going to leave it as an X squared X plus two minus now. You leave the top alone and the drift of the bottom, I mean they use this piece. So I don&#x27;t have to do the product rule is three X squared plus four X. All over the denominator squared. Well if you&#x27;re going to square each, you know, square this function, you can also just write it as X squared squared. So X to the fourth and then X plus two that quantity squared. Um So as you&#x27;re trying to simplify this, which I don&#x27;t know if that&#x27;s really advantageous to do that, but what you could actually do is factor male, do this in red. Um That you could factor out one of these exes. Uh So the reason why that would be beneficial is then I could cancel out uh an ex from all of those pieces. So now in the denominator them down to X cubed. Just think I divide everything by X. Um And then the other thing is you can distribute for X to each term negative one to each term, distribute X to each term, same thing over here as a distribute, distribute, distribute and also distribute them negative to everything. And at the end, when you combine like terms, uh you&#x27;ll end up with Negative -2 x cubed Plus two x squared plus five X plus four, all over X to the 3rd power, X plus two to the second power, and nothing else can be done. So this is a good answer. Will circle it and move on.

Rakesh Kumar Sharma · Answer

the question we have off, friend are consistent for fortune exit Excuse to There you go X squared minus one day We&#x27;re going excess worthless. Thanks for more than first the function Fact rages when reading. Explain this one Do express one. I think that you know I love you need X, you know, express mail. So that begins ing out before this is defined. So he warned me about the radiators Extender X into selecting nexus where okay and us Mr. Election didn&#x27;t. And this week, extended by this one&#x27;s the cool expires actually getting less sex and my miss food derided by yes, and for those of X Let&#x27;s run My Mr by accident is off. What flex differently of dysfunction. Many gadgets, by little signifying formation, hold different station. And that&#x27;s a very good technique. So officiated knows their differences Different station Actually, when we used to go and the physician off minus two y esquire minus to buy extra a week less through by excess fire. So that is that

Rakesh Kumar Sharma · Answer

It is a question if I know that dispensation for therefore fixes assume works, doing it right, except for this one. Okay, so the differentiation of me, that&#x27;s their definition of the new position. You think? Do you know about this? My differentiation of the development. So that would be flex do anyway, sweat off. You know more of his father&#x27;s indifference toward beauty. For Texas. Where? What&#x27;s to free? Who is this? Where must to minus four x Aspire. You are right next to this one. I just find it who minus no excess where I just like this one. So that is a politician.

Yingtai Xiao · Answer

All right. Nice. Try to get the Dura video a square plus X over X minus one. You excuse He comes to X square plastics. The X is because two X minus one curative on you. It&#x27;s because the two x plus one endure If Vivien Leigh seekers tour. So the dirty Oh, why its secrets to no mater. We squared no major. And the new territory just There&#x27;s a few times V minus dear. It will be times you Yeah, he&#x27;s ex clear plus X so their sorries x minus one square, two X square plus X minus two X minus one minus X squared minus X and cancer Just to term. Combined This two terms Look at through Salt&#x27;s ex clear minus two X minus four over X minus one square.

Amy Jiang · Answer

Okay, so the question we&#x27;re asked to find diverted. So since we have the vision of two pollen Orioles, we&#x27;re gonna use our quotient wall. Let&#x27;s live with this as U N B now. Why time that&#x27;s equal to you Prime, which is two X plus one times we and in some shocked the prime. That&#x27;s one times you all over B squared. So let&#x27;s multiply our numerator out. So we have two x squared minus two x plus x or it&#x27;s my sex and then minus one minus X squared minus X all over our denominator. So now let&#x27;s combine like terms we have two minus one cigarettes X squared and in minus X minus X x minus two x when it&#x27;s one all over, X minus one to the power of to

Ernest Castorena · Answer

problem they give us of elects is equal to X squared minus one squared all over X squared plus one. And when we take our river, the blood scene we hate the rid of the top first. So it&#x27;s Chainarong. Well, uh, to times X squared minus one times drinks. And then let&#x27;s see, uh, I won&#x27;t supply by the bottom so we&#x27;ll have an X squared plus one. And then for another term, we&#x27;re gonna need to minus, Let&#x27;s see. I don&#x27;t know. I try to move this over its here about So we&#x27;re gonna track this time taking the derivative of the bottom, which is just two X and most of finding by the top, which is an X squared minus one squared, then all over X squared, plus one to the fourth power. It&#x27;s worried. So let&#x27;s see if we can simplify the numerator a little bit. We can factor out and x squared plus one, maybe even two x. So it&#x27;s plowed two x that an X squared minus one term. So an appointment to see you pulled out the two X and the X squared minus one. So we just have two x squared plus two. And we did a similar thing here. And we only have one more X squared minus one time here, the minus X squared plus one. And this would turn into an X squared. Let&#x27;s see if this was a plus two. And this is a Munsey with science clips my sex squared than Usman me and a boy with X squared plus three. Okay, that looks good. So ended with two x times X squared, minus one times X squared plus three all over X squared plus one squirt. Okay, awesome.

Problem

Find the derivative of each function by using the…

Problem 23 Easy Difficulty

Find the derivative of each function by using the quotient rule.
$$y=\frac{2 x^{2}-x-1}{x^{2}(x+2)}$$

Answer

$\frac{d y}{d x}=\frac{-2 x^{4}+2 x^{3}+5 x^{2}-4 x}{\left(x^{3}+2 x^{2}\right)^{2}}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$\frac{d y}{d x}=\frac{-2 x^{4}+2 x^{3}+5 x^{2}-4 x}{\left(x^{3}+2 x^{2}\right)^{2}}$

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Kristen K.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus