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# Find $y"$ by implicit differentiation.$x^2 + xy + y^2 = 3$

## $y^{\prime \prime}=-\frac{18}{(x+2 y)^{3}}$

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

in this problem. We're doing any question that is expected. That's why plus y straight is free. And where do you suppose it appreciation by second marital question. Let's refined first ever two by taking marriage of old suspect X We have to dance off, boy, We're using four for the second room on the left US I plus extends like time plus two y y prime, is it zero From this we see that Why prime is the negative off to explore. Why divided by exposed to y all right now, using those less find secondary to we're going to use caution. Who? So we have negative? Oh, um two plus y prime. Well, why? Why experts to our minus two x plus y one spike by one plus two y prime invited by exposed to line square. Why prime? Is there any cook too? Negative off. Now we know what y prime is. So we're gonna take this and then plug it in here and plugged up. And right here, whenever you see white crime so we have to minus two Rex was why divide by experts to wire boss *** was too. Why minus to expose Why not spiked by one minus two times X plus y sorry to explosive. Why did right by experts to weigh, uh, you wanted by exposed to warn Spurred we can write this one as viable Prime is equal to negative Oh, two times exposed to our minus true experts Wire looks like Bye three throws experts do I minus two explosive are well liked by X Plus two Why minus two times to expose war He invited by explosives to Why Q. Now why Double prime is the need of negative off three y comes expert to our minus two experts war time saying three x divided by explodes too. Why you and that is equal to negative six times x and four plus X scraped off White spirit divided by exposed to one You Now look at what we end up, what the numerator And look at the orginally question given here. Those are the same. So we know that numerator physical three from the sweet. My unavoidable time to be that negative 18. You're right, but X plus two why Q

#### Topics

Derivatives

Differentiation

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp