evaluate-dydx-at-the-given-points-leftx-y-y2right3-25-y23

Question

Evaluate dy/dx at the given points.
$$\left(x y-y^{2}\right)^{3 / 2}=5 y^{2}+3$$

Doruk Isik · Accepted Answer

in this problem. We&#x27;re doing any question and were asked to use implicit differentiation by very why just X. So we&#x27;re gonna stay there with your old term to expect extent. So let&#x27;s start from the first term we have or execute. It was for the second door getting portable. So we have two extremes. Well, spread plus explore eight times to wine time since Y is a function of X feels happy I d s plus three U S grade. Again wise function X will be happy by the ex again and that is a zero sense. Why is constant? So let&#x27;s cripple terms with Levi the ex left inside. So we have some ideas. Oh, thanks to expert wine plus three Westbourne that is equal to then negative to x Oh, wife&#x27;s Craig waas two squared their promise We don&#x27;t see that very hopeful I respect eggs physical through negative talk to x Times y skirt was to experience the wild by two x squared plus three wire. Uh, sorry to ex Craig. Why? Plus three one square

Doruk Isik · Answer

if this problem were committed in question and where has to use his position? X, we&#x27;re gonna take care of you all the terms of respect. Excellent. Start from first term, that is three X&#x27;s great minus 42nd tour continues over a pool. So we have. Why scrape waas extents? That is first thermal to find their second, which is to buy times D. Why the ex since Y is a function. Thanks. Plus, he had three West prayed he want yet against since one it&#x27;s a record, citing seriousness when it&#x27;s just senseless, brutal. The terms for T y V excellent left inside. He won. Yes. Oh, three y squared minus. You have to explore. Let&#x27;s write old times. We don&#x27;t you idiots on right inside story y squared minus street experience from this weed and see that they would do if I suspect X is equal to one for my mystery inspiring, he wanted by Well, why is it coming? Very bowl. So we collect this one. That&#x27;s one times three. Why minds to fix

Amy Jiang · Answer

Okay, so it&#x27;s funds you Why over TX centers that we have the product of two targets. So if use our product rule, starting with the derivative of X cubed, that&#x27;s three X squared times or remain germ and plus the derivative of Coche so noticed that we have our order function. It&#x27;s too. So we have to kohsh of three X to the power of to minus one, which is one an end times a derivative of kohsh, which is singe of three X and in time, conservative over inside function, which is three. And then times are remaining to him, which is execute. Okay, so let&#x27;s see, we have a three X squared in common and a coche of the X in common. So it&#x27;s factor that out and then we have a coche of X. But to Zinj of three x start, it should be a three X is well, okay, so this is already Oh, this is a situation. Oh, this should actually be an ex left here, since this is X cubed and we&#x27;re pulling out on X squared. So that&#x27;s actually two x

Amrita Bhasin · Answer

We know that you is for my cute, which means that why squared? Do you? Why is negative 1/3? Do you? Which means now we can write this as the constant natives numbered pulled out times the integral of you. The 2/3 do you? Which means the off negative 1/3 terms you to the 5/3 over 5/3 plus seat because, remember But we use the parlor, which means the exploding increases by one. And then we divide by then you exponents and then we back Substitute you is four minus y cute.

Nathalie Luna · Answer

so thiss problem are asked to evaluate this inter from from negative three two negative one of wide apartment to why Over lighted their power What they respect to Why seven? First thing I am going to do here is I am going to rewrite this pentagram. So, uh, yes. So I&#x27;m gonna write it into something more manageable. Something that&#x27;s easier to integrate into. Grand police said it is by a wide to the fifth Power power minus two. Why over there? What? Sil, What? The first thing I&#x27;m going to do since it since the numerator iss its two terms, we can split this up way. Have. Why two fifty power over. Why? Cute. My hands. Two times flag. Okay, over Like you. Next thing is we are going to revise the properties of exponents says so. We have the same base here and different power. Still first excel on top, minus the one and same defense. So this too. It&#x27;s a constant images states right there. And we have put a same base, different powers in this one. It&#x27;s it doesn&#x27;t have any power, but that is actually a one in disguise. So, uh, they have one wasted one minus awesome. No, we just have one less so to simplify. Thes um, these two number silly have Why squared? Hey, minus two times. Don&#x27;t accept one. Minus three that is minus two and Missy away. Why? To my with minus two Bessie parts of this integrate that we aversion Aly had we can rewrite it as this and it&#x27;s the exact same thing set that is going to be my first step here. So since we are not integrating to Santa, we need to keep this here. Don&#x27;t live stout. Otherwise, this equality is a lie. We have hopes that set it, um, actually have weaken substance. This for this. Hey, why is cleared minus two? Why all rights to the minus two? And we are integrating with respect to why so now way have two the int&#x27;l grant. It&#x27;s now two terms each of which iss, a power of the of the variable were integrating with respect to. So what? We&#x27;re going to do this. We&#x27;re going to use the Powerball. So the party says that when we are integrating a power X with respect to eggs that will be equal to X rays to the and plus one divided by plus one plus a constant. If we&#x27;re dealing with an indefinite and took him in this case, we are not. So it doesn&#x27;t really matter in this case, But this with the parable says And it can be well to minus one for dividing by Cyril Reasons. So, um, when we&#x27;re integrating apart of X, which is at one to the power Uh huh. And then divide by this new power that&#x27;s we&#x27;re going to with each turn Sit next up, we are already integrating. So we don&#x27;t need to write this any more. Silly White, too, because why to press one That&#x27;s three. And we divide by this new power. That&#x27;s three minus two. This stays the same. And this why becomes Linus two plus one that&#x27;s minus one. And we need to find like this you power and thiss iss evaluated from y equals tube. Why equal to minus three until minus one? So we can too. Some adjustments here. Okay. Would you rewrite this and this way, So White day over thing I don&#x27;t think we can too much about it. So we&#x27;re just gonna not touch that friend out now for this part. Why base to No way. This minus one. We can two divided by one is too. And this minus. And this minus combined to a plus this Tuesdays office. And this. Why? Since it isthe negative at the parts negative one gets, say, mass. Why? To the first power here, which we&#x27;re not going right. And now this. It&#x27;s evaluated from what? Equal to minus until one. Linus, my stay up in time. Okay, so next thing that we&#x27;re going to do is we&#x27;re going to evaluate this part. Great. So take care of the sport. We&#x27;re going to value this whole expression. When? Why? Who&#x27;s minus one? And then we&#x27;re going to subtract this whole thing again. But when? Why equals mainstream celeb start first one, why is minus one? So we have oh, minus one cube over three last over. Why? When? Why its menace already. So it&#x27;s first print. Now subtract the same expression evaluated on y equals minus three. Sit. Why that this minus three Q over three. Alex, keep groups Q over three less two over. Why, that isthe negative three already. So now we work on simplifying this. We just have numbers I know we don&#x27;t have any more variables. All right? So prejudiced to terms, Way are going to recall a fun fact fun kiss. It&#x27;s useful so far means and laugh. And when we have a power of a minus thanks, that was you. That that could be equal to one of two things can either be x squared or minus X squared. So with this, this means minus whatever this number is. Uh, so it&#x27;s equal to this When? And the power is even and equal to this when in the power&#x27;s on. So with that in mind, we are going to take care of that. So since it is, we have three. It&#x27;s an odd power between sis is equal to minus one. There, one cube over three on. So we have two divided by minus one that&#x27;s minus two minus. So let&#x27;s give the separatist for now. Do not confuse ourselves, huh? So again, give us in out power. So the sequel to Linus three cubes divided by three from this to owe. So this might have something We can put it out here, right? So no, no. Make things easier, right? Soup? What else can we do here. This one cube is the same. This one. It&#x27;s the same justice equal to one. And this three cube on that means three multiply fights off three times divided factory. Which means we take away one piece and that is all we can do. So again, rewriting. We have minus one third, minus two. So we have this minus this. Finest, that&#x27;s close. Three race. You three minus one that&#x27;s cleared. And this minus this minus until this minus. This kind of distributing itself over him. That&#x27;s a plus two. Derek ofsome um, so no. Oh, we have to. To add all these, we want everyone to have a coefficient of not proficient in the murder of three. So do you want this to be over three? So that means we multiply it through here and this one, we Underwood just sit still. We go back to three. Everything okay? So now we can add all these together. So the generators three. Which means that three states there, we don&#x27;t sum or multiply or anything. And we take care of all these. We have minus one minus two times three. That is six plus three Q, that is twenty seven plus two. All right, so this number in the end, I had this twenty two over three. So soon? Yeah. We have finally made it, um, thiss into grow evaluates to twenty two. All right?

Doruk Isik · Answer

police it Derivatives are taking the route. You both sigh with respect to X The term we use the product rule the ripped off a Y square We use Cheryl. I use who I promptly denote. The wide the X corruptive. Why Cuba used Cheryl Ryan side. We get zero. So why prime? It was minus Freud&#x27;s cubed minus to exp i square you have square y plus rea y square.

Problem

Evaluate dy/dx at the given points. $$x y^{2}+3 x…

Problem 26 Easy Difficulty

Evaluate dy/dx at the given points.
$$\left(x y-y^{2}\right)^{3 / 2}=5 y^{2}+3$$

Answer

$\left.\frac{d y}{d x}\right|_{(5,1)}=-3$

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Basic Technical Mathematics with Calculus

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$\left.\frac{d y}{d x}\right|_{(5,1)}=-3$

Basic Technical Mathematics with Calculus

Grace H.

Heather Z.

Samuel H.

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.

Samuel H.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus