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Find the value of the derivative:dy ify=9 - 8x2 dx Ix= ~2dy dx Ix= - 2(Simplify your answer:)...

Question

Find the value of the derivative:dy ify=9 - 8x2 dx Ix= ~2dy dx Ix= - 2(Simplify your answer:)

Find the value of the derivative: dy ify=9 - 8x2 dx Ix= ~2 dy dx Ix= - 2 (Simplify your answer:)



Answers

Find $ dy/dx $ by implicit differentiation.

$ x^2 - 4xy + y^2 = 4 $

This problem were given any coercion. And when asked to use its transition to find out why it's almost like they were going home. Time to suspect X. We have 46 That is what first gives us. Plus, pregnancy is perfect for second term. So you have boy plus X times B Y E s minus two times one time for your e X. Since Y is a function of X ELISA defendant Grable and that is equal to zero since record and scientist sense. Unless you're holding firm with you I d x On one side of you I d s, um, exploits to Why he's it. Goto Negative four x one The firmness we see that they're moved. Your boy is an eagle to negative off or exports more divided by ex minds. To what? Or you can write this one. As for exports, why you like to why my specs bull or right

Here The implicit derivative. So by thinking that the remedy from both sides Ah, here we use a product Rosa y plus X, The ribs have wise. Why prize? Why prompted the naughty white yaks? And this will be like this right hand side Should be zero y prom should be X minus two. Why numerator raise miners for X minus y

51. We're gonna find the derivative diva over DX by the French hating implicitly. So let's appreciate both sides. We have two word devour the excusing the power change rule Over here on here. We're gonna use the ocean. True. So we have the denominator square denominator. Different station of new monitors to X minus Numerator difference. Ishan of denominators. Two weeks. This comes orders to from both the sides. If we divide the school counselor, what are we left? Furthers Weir. D y over d X is equal. Do it's Open up the records. So we have X cubed plus x here minus X cubed minus X year over X square plus one old square. Okay, so this comes out as X Cuban minus six cubits canceled. And what are we live for? This? Why'd divide over TXs X minus minus Access to X or X squared. Plus one whole square is as it is, integrating both sides by y we get the value to get the expression for diva or the excess two weeks over extra square, plus one full square times. Why This is the final answer

So for this poem, we're gonna have to use quotient rule to perform inputs of differentiation because what we have is X squared over X plus. Why equals y squared plus one. So I'll take the derivative of both sides when we take the derivative outside's, we have to use the quotient rule on the left side. So it's going to be, uh, the low or the numerator times the derivative of the numerator, so tend to x and then, um, minus X squared times he derivative of X plus y, which we know is going to end up being one plus. Why prying that Obama. I'll be in parenthesis right there. That's what we have going for us. Then, Um, what we'll have is that this is equal. This is all over the denominator squared. So I close, why squared? And then this is equal to We're gonna want Thio do change again. Why Squared will give us two y times y prime plus zero because one is just constant. So this is what we have. Then we can multiply both sides by X plus y squared. So multiply that on both sides and what will end up getting as a result, is this Times X plus y squared. Then once we do that, we can add X squared plus D Y d. X on both sides. And the reason why we can do that is because we end up getting the two x times X plus y minus X squared, minus X squared times. All of this. So when we subtract X squared d y d X from both sides, what will end up getting is a two x squared us two x y minus X squared equal to to why x plus y squared plus X squared times D Y d x or just white prime, then dividing both sides by two y times X plus y squared plus X squared. We will get rid of this right here. And then we will have this all being divided by this value right here. So that is our white crime.


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