Problem

$$x y^{2}-4 x^{3 / 2}-y=0$$

07:54

Problem 21 Easy Difficulty

$$x y^{2}-4 x^{3 / 2}-y=0$$

Answer

$$d y=\frac{1-y}{3 y^{1 / 2}+x} d x$$

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Calculus 1 / AB

Thomas Calculus

Chapter 3

Differentiation

Section 9

Linearization and Differentials

Discussion

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Video Transcript

look in this problem. We need to find de wide the French fly, knowing that if wise fix then the wise the derivative of X times the differential, uh, in the problem we don't have war defined is therefore Vicks. We have implicitly define why in the form of two y to the power of three half plus big. Why Martin thank equals zero. So to find the derivative off the function, that is why so why the river is there? Six. We will ah, the French at this implicitly remember, Why is wired Vicks for any any term containing why you've going to be a composition off while wicks and what happens to the term? Like I said, for example, why to the power of three, uh, cars means that we have a composition off these two factions and we need to find the riveting for we are doing implicit differentiation here. We basically have you off. Why? Off x ah, by chain rule, the derivative of this is but they're a bit of a view calculated in why on then, we have the well, Warren, you off X is raising things to the power of three house. So the roots of a view of X is going to be three homes. Times X, uh, this morning swarm to the one car would have we done here. We have used the power of X to the power of end. The route is in times X to the power off reduced, exploding by one. According to this power room is going to be three. Have so you Oh, wine off big the route. You've three hearths times. Why? Through the power off one, huh? Times but there to avoid 23 Why? To the power off one, huh? Burns with the route to avoid the second term involved, uh, again you off x times the x where via vexes function y Vicks. And you're 66. So by the product rule, this is gonna be, uh, during a few times, three. Plus you. Time of it, Which is the narrative of exits. One B is why the U is x times the derivative. Why is the derivative before? So we have bluff. Uh, why love x times? Why the relative? And finally, to derive this the root of X x of the power one is what it Vera, we are going to help people for this bit. So you we affect around. If we effect throughout the there to avoid from these two turns, we will be left with three. Why? To the power off one bluff thick. All right. On the terms not containing with derivative before I are. Why more? This one here A worship this over to the other. Fired by adding one Martha Warren to either side. And we have more squared three to the power of perfect here. On Why? By dividing with parentheses Why the French? Straight to you one minus y three. Why? To the power of one perfect food. What would divide be the Why would be this time? One minus y three to the power. Why open her? Uh, that should be there. Problem of hands. I hope it helps few. So

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