5

6. (12 pts) Find +X =Yyusing implicit differentiationNote: You may not need all this space below to find lengthy problem!it is not...

Question

6. (12 pts) Find +X =Yyusing implicit differentiationNote: You may not need all this space below to find lengthy problem!it is not

6. (12 pts) Find +X =Yy using implicit differentiation Note: You may not need all this space below to find lengthy problem! it is not



Answers

Use implicit differentiation to find $d y / d x$.
$x^{2} y+x y^{2}=6$

All right, We are asked to find the first derivative of this function through the attributed of Lie with Respect, X. And we have to do that using implicit differentiation. Because we can't solve this for why, and just have y equals and expression vex. So as we're doing this, we're gonna have to remember the product rule because we have things multiplied together. And remember that we're taking the derivative with respect to X. So the driven off the first term remember the product rule? It's the first function X squared times, the derivative of the second. And I hope you don't mind. I'm gonna use the wide prime notation instead of D Y t X just because of taking up space Here on my screen is I'm writing this up. So first times the driven off the second plus a second function. Why times the driven of the first derivative of two x of x squared with respect to X is just two x using the power plus Now the same thing here. First time's the driven of the second, Which would be to why live prime plus a second times. The derivative first derivative of X is just one equals and the derivative of a constant is zero. So now we want to collect our terms with Y prime in them on one side and our other terms on the other side. So we're going to move those two terms over to the other side of the equation. And since both of these terms with the UAE prime have just a Y primary, I can factor out that common y problem. So that will give me X squared plus two x y times y prime on the left side of the equation. And that's gonna equal. When I move these over to the other side, I'm going to subtract him. So it's just changing their signs. Not all equal to negative two. X y change my signs minus y squared. And now, to get the wide crime by itself, I just have to divide both sides by the X squared plus two x y. That means that why prime or do I d? X if you prefer that notation is gonna equal negative two x y minus y squared divided by X squared plus two x y

Here we have to find an implicitly for differentiation, often equation, which is extra square. Where? Let's x y square secret of six. So let's differentiate board sites were getting be over E X off square. Why, plus ex wives where this will be for D over DX off six. So this becomes d over DX off excess where and this becomes be or the ex off X y square on defense station off concerned zero. So this further becomes now over here we have to use a productive. So the Fallston remains advocates and we defend shared the second that the second of remains as it is. And then we differentiate the first. Similarly, in this the upper use a product room. The 1st 1 remains editors. We differentiate the second door, Then the second under means are the cousin. We differentiate Fallstrom. This is equal to zero. So this becomes extra square be by awardee X blessed Why Defense station of Excess square with two weeks plus x times, differentiation of I square will be to buy on. People also have devoured years Bless vice one and defense station of extra everyone. So this becomes equal to zero Now this further becomes let's club the terms which have devoured the X. We take, devour the excess former, then be a having extra square over here and do X. Why over here from this, then we have the remaining tones as two X Way, which is this. And then we have the White Square, which is this. This is equal to zero. So let's take these two terms over to the rates of the are getting devoured e x x squared. Let's to expire will be four to minus off two weeks. Why minus y squared simples becomes even over tea it's will be. Divide both sides by this expression, so get device or D excess minus off. Do X Y Yes, Why square over X square best struck next. So this will be a final answer

Hello. We have to find the virus. And you have to evaluate the virus at the indicated point minus one comma two education is given to expire plus y plus two who works? Why plus y plus two? Yeah, maybe close to zero. Okay. At the point. Yeah, man is one comma. Two. Yeah, Yeah. Mhm. Yeah, I want this man is one common food. Mhm. Yeah. So we will use implicit differentiation and like that with respect to the X. So we used to handle here. Right? That is two of X levi x upon the X. Let's go to our white less diva of exit Pontiacs. Because 20 from here we can try to express one. What is Let's do what it cost to zero providers will be cost too. Minus of Dubai upon one Plus who works Okay. Yeah, Thanks. Mhm. This is a function of ideas. X Nevada's at the given point. My name is one comma two So it will be close to minus so forward upon one is one. Yeah, providers at the given point, man is one comma, two will be cost too. Four. I hope you understood. This is the value of bad is this is the functional bodies. Thank you

Hello. We have to find the virus and evaluate the virus at the given point. The equation is x Y minus six equals two zero. The point is to commentary, so we will use implicit differentiation. Mhm implicit differentiation with respect to X. Yeah, because it will be D v X upon the X plus by of X. Yeah, that is one close to zero. Yeah, So providers will be equals two minus of eye upon X. This is a bodice and the riders are going function. Good point. That is two comma three. Will you go to minus of three? I do. I hope you understood, Mrs Answer. Thank you.


Similar Solved Questions

5 answers
Zonsider the subspace W of M22 defined by W span ([1%] [? 3]) Using the standard inner product on M22 , find an orthogonal basis for W .
Zonsider the subspace W of M22 defined by W span ([1%] [? 3]) Using the standard inner product on M22 , find an orthogonal basis for W ....
5 answers
For the reaction shown below, draw a mechanisms that explain the formation of both productsOCH;CH;OH;OCH,
For the reaction shown below, draw a mechanisms that explain the formation of both products OCH; CH;OH; OCH,...
4 answers
Can this differential equation be solved using separation of variables?dy 10 _ %y + 9x drChoose ansver:YesReport
Can this differential equation be solved using separation of variables? dy 10 _ %y + 9x dr Choose ansver: Yes Report...
5 answers
Ammonia Water2. H-1. KMnOj NaOH; heat 2.H;o- SOClz
Ammonia Water 2. H- 1. KMnOj NaOH; heat 2.H;o- SOClz...
5 answers
One-half ampere flows through a 40-ohm resistor.(a) How much power is being used?(b) How much is the voltage across the resistor?
One-half ampere flows through a 40-ohm resistor. (a) How much power is being used? (b) How much is the voltage across the resistor?...
5 answers
Solve the system by using each of the three methods: (a) the graphing method, (b) the substitution method, and (c) the addition method.$2 x+y=1$$-4 x-2 y=-2$
Solve the system by using each of the three methods: (a) the graphing method, (b) the substitution method, and (c) the addition method. $2 x+y=1$ $-4 x-2 y=-2$...
5 answers
What is the angular speed of the Earth's center of mass as it orbits the Sun?
What is the angular speed of the Earth's center of mass as it orbits the Sun?...
4 answers
Ktis a complete graph with 4 vertices; and C- is a cycle with 7 vertices Suppose these share 3 vertices. How many distinct edges will there be in KU Cz assuming the shared vertices area) 3 Consecutive in the cycle2 Consecutive and otherNo two vertices are consecutive
Ktis a complete graph with 4 vertices; and C- is a cycle with 7 vertices Suppose these share 3 vertices. How many distinct edges will there be in KU Cz assuming the shared vertices are a) 3 Consecutive in the cycle 2 Consecutive and other No two vertices are consecutive...
1 answers
Write each function as the composition of two functions. (There may be more than one way to do this.) $$ y=\left(3 x^{2}-7\right)^{2 / 3} $$
Write each function as the composition of two functions. (There may be more than one way to do this.) $$ y=\left(3 x^{2}-7\right)^{2 / 3} $$...
5 answers
Blue light incident photon λ=463 nm scatters offan electron at rest and change direction of motion by θ=30. What isthe change of wavelength? Is the outgoing light stillblue?
Blue light incident photon λ=463 nm scatters off an electron at rest and change direction of motion by θ=30. What is the change of wavelength? Is the outgoing light still blue?...
5 answers
Find $ if" = Vsr + V"+v8 Hint Let v = Vsz +%z), g(r) V+TG). h(r) V8 -
Find $ if " = Vsr + V"+v8 Hint Let v = Vsz +%z), g(r) V+TG). h(r) V8 -...
5 answers
Use the given degree of confidence and sample data to construct a confidence interval for the population mean u. Assume that the population has normal distribution; n = 50_ x = 74.6, s = 11.5,99% confidence level. Hints: determine if the 0 is known?
Use the given degree of confidence and sample data to construct a confidence interval for the population mean u. Assume that the population has normal distribution; n = 50_ x = 74.6, s = 11.5,99% confidence level. Hints: determine if the 0 is known?...

-- 0.028623--