find-the-derivative-of-each-function-by-using-the-quotient-rule-yfrace2x3-x-5-2

Question

Find the derivative of each function by using the quotient rule.
$$y=\frac{e^{2}}{x(3 x-5)}$$

Gregory Higby · Accepted Answer

All right, We are given why equals e squared all over X times three x minus five. Uh Now we are going to do the quotient rule, There&#x27;s a quotient in there um but before I get started, just remember that E squared is a constant. And why am I bringing that up is because the derivative of a constant is zero. So when I go to take the derivative using the question rule, Um the derivative of the top is zero. That&#x27;s what I&#x27;m trying to get at. Um And you leave the bottom alone and then minus. Now you leave the tap alone. But notice as we do the drift of the bottom, we have the product rule. So you have to do The quantity of the derivative of X, which would be one. You leave three X -5 alone. And then plus, that&#x27;s why I put in parentheses, we have to distribute. I guess I should have put parentheses right here. Yeah, because you got multiplied by both pieces, um then leave X alone and then times the derivative of three x minus five, which would just be three all over the denominator squared, just square each piece you&#x27;ll be fine. So as you notice this zero times anything will be zero, so that&#x27;s gone. Um I can actually simplify inside here that I have three X plus three X six X uh minus five. Uh So let&#x27;s actually leave the problem like that because nothing fancy is going to happen. So I&#x27;m gonna write my answer like this negative of E squared Times The quantity of six x -5 all over that X squared three x minus five squared because again nothing canceled. So this should be good answer for you.

Amy Jiang · Answer

Okay, So its able to following you and this as B and use our quotient able to find our derivative to have white crime is equal to, um you times that six x months one times the that&#x27;s two x minus 12 par five and that&#x27;s minus B prime were using the chain role here, So that&#x27;s five times two x minus one. Depart for kind of preservative over inside that to in times you we x squared minus X all over B squared, which is two x minus one over R five to fire, too, and that&#x27;s 10.

Rakesh Kumar Sharma · Answer

in this issue. I know the most of the people. Deforestation off function affects is you assume Texas. Where where? G us five. By access for the first day, they were defusing. Moaning are who? X, my tea and the precision off. This will be if you could take excess firing. Doing the best that b minus two times. Oh, just about this one in five. Okay, The sensation for this With me who exploit three minus. I execute that position for you.

Robert Daugherty · Answer

problem number 27 Section 45 Again, Everything in this section deals with finding derivatives of functions that involve logarithms. So here I have. Why is equal to e to the five X divided by the natural log of three x each of the five x over the natural log of three to the X. So again, guiding principle here I&#x27;ve got something that looks like y is equal to F over G. Why prime is quotient rule F prime G minus G prime f over cheese squared. In my particular case, eat of the five x represents F and natural law. Go three x represents a g. So to go find this derivative. So why Prime is going to be equal to F Prime G. So the derivative eat of the five X is five e to the five X so that&#x27;s F primes, Then times G. That&#x27;s gonna be times natural Log of three x minus G prime f So g prime f. That is gonna be what one over three x times 32 That&#x27;s G prime. All of that times F, which is either the five x over G squared, which is Ellen of three x squared and it looks like I can simplify a bit by multiplying everything by five X. And so I multiply everything by five acts she meet motive, everything by X because what you&#x27;re going to see here? I&#x27;ve got three over three I can keep from having a complex fraction if I multiply everything so by X so I&#x27;m gonna have five x e to the five x natural log of three X and then minus E to the five x over X natural log of three X and then all of that is squared and it looks like I could probably factor out and eat to the five X, um, for a further simplification. So if I were to do that, I&#x27;m gonna have e to the five X and then I&#x27;m left with five x natural log of three X minus one, all of that divided by X natural log of three x squared. So each of the five x five x of natural log of three X minus one over X natural log of three x All that quantity squared

Amy Jiang · Answer

Okay, so before it&#x27;s a conservative, I&#x27;m gonna be right the following as a negative exponents. So that&#x27;s extra. No. One extra pair three plus five. And that&#x27;s equal to X to the power of to plus five x Department one. Now take the derivative of the fallen. So I get two X drive to minus one plus negative one times five extra perfect one minus one so that use me to X plus. Actually, that&#x27;s minus five x negative two is equal to f prime of X.

Alexander Wittmond · Answer

Okay. We&#x27;re finding the derivative of Y equals Ellen. Five. Execute minors to X to the free house. First thing where you probably want to do is to use the power rule for longer thems to simplify things for our cells and pull out that free has as a multiple or a product. Okay, Now we&#x27;re going to use the power. So we get y prime people&#x27;s free up free house. Times one over five. Execute minus two X Times five executed mass to X trying, which is equal to three House times fifteen X squared, minus two over five. Execute minus two books. Okay, come on. Really?

Problem

Find the derivative of each function by using the…

Problem 18 Easy Difficulty

Find the derivative of each function by using the quotient rule.
$$y=\frac{e^{2}}{x(3 x-5)}$$

Answer

$\frac{d y}{d x}=\frac{5 e^{2}-6 e^{2} x}{\left(3 x^{2}-5 x\right)^{2}}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$\frac{d y}{d x}=\frac{5 e^{2}-6 e^{2} x}{\left(3 x^{2}-5 x\right)^{2}}$

Basic Technical Mathematics with Calculus

Grace H.

Heather Z.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Heather Z.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus