use-implicit-differentiation-to-find-an-equation-of-the-tangent-line-to-the-curve-at-the-given-poi-2

Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
$ \sin (x + y) = 2x - 2y, (\pi, \pi) $

Frank Lin · Accepted Answer

so equation of the Tenderloin We find that the river through first So take the room tea With respect to X we get close i x plus y times that the root of inside it was to my to my prime So why prime should be to minus cose I x plus y older, um two plus six course I x plus y So that tells us at pi pi close on two pi the same iscause zeros one so slow you cause two minus one over to pass for this for Norris three. So equation should be y minus. Why my pie or slope? Times X minus pi. And then you can simplify this sort of baby if you want.

Doruk Isik · Answer

in this problem, whereas to use himself differentiation by any question and lying to the Given her at this given point by over two or all right, we know that the question of tension line will give off my minus point out. Where fire force, when a times slow. So what we do? We talk dysfunctional it that extra five times explains. That&#x27;s not or it&#x27;s not as if I were to. So let&#x27;s use implicit differentiation. Take. There were topless, given a function. He have two terms consigned to X and y plus y prime site to eggs were used for a cool that is equal. Do pro sign up to our minus two x sign to war. On what crime? We can grow old terms by primal What side? So we have white crime to X sign to one once signed to X, and this is equal to co sign to Why minus two. Why co sign to x promise. We see that why prime is equal to, um, go sign to boy minus two. Why co signed to X He wanted by two x sign by plus side to X. Now let&#x27;s elect this. There were two at this given point, we find and Verity what prime at that point to be co sign of fire to minus two pi over four co signer by he wanted by two times prior to signed by or to my son by put some plywood to zero sign of 00.0 on this we see that. Why prime is that one? How of people? I&#x27;d be directive in this equation of attendant Lane. We don&#x27;t find out why. Minus fiber. Four. Is it on how x minus fired two From this time be question of transatlantic forgiven point is, why is it?

Doruk Isik · Answer

in this problem rescues and present the transition to find the question of defensive line to the given tour at a given 0.1 Health. We know the question of one will be up for y. Minus or not is director of dysfunction of a little argument point? Excellent times explains. It&#x27;s not so in order to find the question the personally to pack light or find derivative related given 40 So to do that last time David off all the perfect suspect X we have to expose to wine times why prime that is equal to two times two x ray plus, um, to Weisberg when it&#x27;s X times. Now there was a look in your function, which is four X plus four. Why times y prime minus one. All right. In order to find directive at people that that given point Les Plus X not on a warning in. So we have zero plus one crime that is equal to two times zero plus one. Hell, uh, my zero. That&#x27;s like by zero plus two. Y pine likes one from this. We see that Why prime is equal. One off course. This is they were to ever let that given 10.0. Now, since we know this less like what your envy have Wyman&#x27;s health is a photo one Times X minus zero Promise me that when the question of friends let s x plus one.

Amrita Bhasin · Answer

this question asks us to use impressive differentiation to figure out what the drift of this and on the tension line. Okay, we&#x27;re gonna be using the Jame rule on the term Why squared and then what&#x27;s in parentheses to X squared Plus two. I scored minus X Prince C squared two acts is the derivative of X squared plus two wise, the derivative a y squared times. Why prime make the expert at the new proficient What&#x27;s in parentheses stays the same and take the derivative to X squared. The derivative is for acts derivative of two. I squared is for why? Why prime minus one? Because the derivative of negative X is negative one not when X&#x27;s year on Why is 1/2 this means we can simply pull again plug in the values x and y into what we just figured out. This gives us why prime is two times 1/2 times to y prime minus one which is equivalent to simply one is why prime. Okay, now use point slope form. We&#x27;re looking at the 0.0.0 1/2. Therefore, why minus 1/2 is one times X minus zero, which means why is simply X plus 1/2

Heather Zimmers · Answer

Let&#x27;s find the equation of the tangent line to the curve y equals sign of sine X at the point. Pi zero. The slope of the tangent line will be the derivative at that point. So let&#x27;s find the derivative. And we need to use the chain rule because we have an inside function and an outside function. It&#x27;s a composite function, so the derivative of the outside the derivative of Sign is co sign. So we&#x27;ve co sign of sine X times. The derivative of the inside The inside is sign so times coastline X. Now we want the derivative evaluated at pi. We don&#x27;t have to simplify. First, we can go ahead and substitute the pie in there right now. And we have co sign of signed pie Times CO sign pie. Well, the sign of pious zero sweep co sign of zero and the coastline of pie is negative. One. The coastline of zero is one, so we one times negative one. So the slope is negative One. Now, To find the equation of the line, we can use point slope form. Why minus y one equals m times X minus X one where the point X one y one is pi zero. So we have y minus zero equals Air Slope negative one times a quantity, X minus pi. Let&#x27;s simplify that. So we have. Why equals the opposite of X plus high. That&#x27;s the equation of the tangent line.

Amrita Bhasin · Answer

this question gives us why is sign of sign of acts and the point pie Comma zero. First step is we need to find the derivative because the gold this question is to find the equation of the tangent. We need to find the derivative first. Okay, we know the derivative of Sign is co sign and then we know, but we maintain the sign of acts. So instead of sign of sign of X, the derivative of Sinus co sign of sign of axe and then the derivative of sign is cosign of ex again. So this simplifies are derivative to be co sign of acts Times Co Sign of sign of axe. Okay, now we have the point pie comma zero. Therefore, plug in pie. There&#x27;s some plus two negative one time to plug into point slope form. Given the point, Pikom a zero. Why? I&#x27;m honest hero is negative one, which was our m. We just figured us out in the previous slide. This simplifies to express wise pie

Frank Lin · Answer

in this problem were given occur and where students our position by me. Questions like that Given point Pi pi tasker You know not the equation of men&#x27;s line will be on y minus or not times their job dysfunction of With that beginning point. Excellent times explains. It&#x27;s not were this is one up in this point, everything&#x27;s not Celeste. I gave itto or times would respect extent. We have hopes I&#x27;d expose why times their report. Inter functions are needy Ex off exports Boy is it to minus two. What prime, Um that is co sign exploits y times. Why Prime plus Warm Is it a two minute July prime? Let&#x27;s group all the terms with my primary once I&#x27;d be. How y prime two plus co sign experts. Why is equal to two minus co sign exports? Why from this? We don&#x27;t see that. Why prime? As to minus cup Sonics before divided by two plus toast sanded off Fine. I&#x27;m like demon extent and one instant catfight. Quite firm. We see that boy primed is equal to two minus coast on to pine, divided by two plus. Come sign to five that is a worn off free. If you play everything in to the question of tens of land we have women&#x27;s are is equal to explain a spy from thy sweet and see that because your life is a very X plus two pi over three.

Problem

Use implicit differentiation to find an equation …

Problem 26 Easy Difficulty

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
$ \sin (x + y) = 2x - 2y, (\pi, \pi) $

Answer

$y=\frac{1}{3} \cdot x+\frac{2}{3} \pi$

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$y=\frac{1}{3} \cdot x+\frac{2}{3} \pi$

Calculus

Grace H.

Heather Z.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartCalculus

Grace H.

Heather Z.

Caleb E.

Samuel H.

James Stewart

Calculus