find-the-derivative-of-each-function-by-using-the-quotient-rule-ufrac4v2-2

Question

Find the derivative of each function by using the quotient rule.
$$u=\frac{4}{v^{2}}$$

Gregory Higby · Accepted Answer

as we&#x27;re looking at this problem, you actually don&#x27;t need the quotient rule to get the correct answer. So kind of a as a side note, you could actually just know the rule of exponents um that that&#x27;s equal, so then D. U D V would be equal to negative eight beat the negative third power, which I&#x27;ll explain anyway. So identify your quotient right there. So when you do the quotient rule, D U D. B. You take the director of the top which is zero and you leave the bottom alone, which is actually just that minus. Now, you leave the top alone. Times the derivative of the bottom, all over the denominator B squared squared. So you probably notice that zero times anything is just zero. So what I&#x27;m left with is negative eight B. And when you take a power tool power, you multiply the exponents. So two times two is four and just think about it. It&#x27;s the same thing as negative eight B. With four B&#x27;s on bottom. So you could cancel out uh, one of those V&#x27;s. So the correct answer, as I mentioned earlier is going to be negative eight over B to the third power. So that&#x27;s your correct derivative. Um And I guess the work on the left is the quotient rule, but you didn&#x27;t actually need it to get the right answer.

Ernest Castorena · Answer

for this problem. They give us the function after Lex is equal to four to the negative X ray. And while it seemed we&#x27;re going to need todo General for this who have a primary X is equal to well, we were based to a part of the natural. Ah, go to me times the exponent function. But our power is a composition. So we&#x27;re gonna need todo Chainarong Love Negative two x yet I mean the boy with Let&#x27;s see, negative natural log of hey, times x times for so the negative export and I did was bring the steam into the natural log report using properties most fly by okay.

Ernest Castorena · Answer

this problem. Let&#x27;s see, they want us to find the derivative and we can use the question room. So take the derivative of the top three Expert multiplied by the bottom X squared plus four squared. And now subtract this time, Leave the top alone. Take that area with the bottom and we&#x27;re gonna use change over that because we have input squared. It&#x27;s a lot of B two times the input times the root of of the input, which is the Times and other two X. And all of this will be over X squared plus for to the fourth power since we squared it again and unseen. When we take our derivative, we want to say a derivative is equal to this Are old function was over here and I grab it was over here, So let&#x27;s see. Looks like we can pull out of next to the fourth before anything else, a factor went out. This will end up being to the ones Piron. This won&#x27;t have any. And this will become cube. So we&#x27;ll have. Let&#x27;s see three x to the mm. Is there a chance of this of even know we&#x27;re never three x to the fourth, uh, strong export. And then we&#x27;re gonna want to subtract four X to the fourth and then all over X squared, plus four que And now on the 12 x squared, minus X to the fourth and then all over X squared, plus y cubed awesome.

Ernest Castorena · Answer

thank it This time. Make it was the function of the X is equal. It&#x27;s X squared plus four all over X Cubed squared. Well, actually, this is X squared plus foreign over X to the six that separate the fraction next of the six. So you end up with X to the negative worth plus for X to the negative six. And then we can just the empire on that. We&#x27;ll end up with negative for X to the negative and then my ass 24 next to the negative seven.

Louisa Benatovich · Answer

here we have explored over Cosi Ghent to the fourth Ex, so we&#x27;ll do a little bit of rewriting. That&#x27;s the same as saying X squared over. Co see Ghent X to the fourth. I like writing it like that. It&#x27;s more sense of my brain, but it&#x27;s still a fraction, and that means I would have to use the question and I try to avoid the quotient rule whenever possible. So I&#x27;ll do a little I&#x27;ll rewrite. It was multiplication, so we would have instead of the fraction we&#x27;d have X squared times Cosi Kent X to the negative Fourth. Because remember, the negative exponents turns it into its inverse a fraction. Now we can use the product rule, which I enjoy it so much more. Remember that that&#x27;s the first time. So derivative of the second plus the second times, the derivative of the first. This is the first. This is the second. Okay, lets start the process. I have a friend. Lex equals the first is X squared times the derivative of the second. We use the power rule Bring negative four down sheep This variable the same coasts. He can&#x27;t x negative for minus one. That&#x27;s negative three and then we take the derivative of the function on the inside. Remember that the derivative of co ck an axe is negative. Cosi can&#x27;t x coat hand x something that you&#x27;ll end up memorizing more use. So then we have times negative. Cosi can&#x27;t x co 10 X now that is long and crazy. What? We finished the first section plus the second, which is just this at this point, the second coast, you can&#x27;t X like the fourth becomes a derivative of the first, which is simple power rule stuff she squared is two x her feet. Let&#x27;s rewrite it. Combined terms make it look prettier. So this whole section is the first part. So I see that we&#x27;ve got to a negative signs those will cancel. And then we&#x27;ve got a fraction No, we have a negative exponents, so we&#x27;ll want to send him back down below. And then we got all our non fractional turns for you. So what I&#x27;ve underlined in red goes on the top, At least complicated function goes in front four X squared coast. He can&#x27;t x co 10 x and then because this is to a negative exponents, we send it to the bottom. Does he can&#x27;t x All Cube. This is our second portion over here saying kind of concept. Hey, could the negative exponents below close again? Thanks to the fourth told. The choice of that, my friends, is your final answer.

Ernest Castorena · Answer

they give us this function and we should write it into a form we can more easily handle. And now we can take the derivative. Well, let&#x27;s see. Pyro list Spring the power down. Well, Underwood negative. Eight of the negative fifth, and for the second time we&#x27;ll have negative X squared.

Problem

Find the derivative of each function by using the…

Problem 14 Easy Difficulty

Find the derivative of each function by using the quotient rule.
$$u=\frac{4}{v^{2}}$$

Answer

$\frac{d y}{d x}=-\frac{8}{x^{3}}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Caleb E.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{d y}{d x}=-\frac{8}{x^{3}}$

Basic Technical Mathematics with Calculus

Grace H.

Caleb E.

Kristen K.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Caleb E.

Kristen K.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus