find-the-derivatives-of-the-given-functions-2-tan-1-yx23-x-2

Question

Find the derivatives of the given functions.
$$2 	an ^{-1} y+x^{2}=3 x$$

Tyler Moulton · Accepted Answer

uh huh. We want to find dy dx for the equation to our 10 Y plus X squared is equal to three X. To solve this, we need to find the derivative shortcuts that are most relevant to this problem. In particular, we&#x27;re going to utilize our recently learned invested in metro derivatives to solve. So I have listed here the three major inverse trig derivatives in particular. We need to use GPS are TNX 1/1 plus X squared. But it&#x27;s problem. We also noted the chamber product rule and so on for this problem. We need to also definitely use the chain rule because we&#x27;re gonna have to use implicit differentiation and this is not a simple function of Y. So by implicit differentiation we have D D X R T N Y times two plus X squared equals C D S three X. Now we take the derivative with respect to X. For each function where every term of Y has a dy dx by the chain rule. So we have two dy dx over one plus Y squared. R channel two. Archie Ny or rather derivative our to our D n Y plus two X equals three, solving for new i d X gives you, I d x equals one half times three minutes to X times one plus Y squared.

Todd Vawdrey · Answer

Okay, So this problem, we&#x27;re finding the derivative of the tan squared X. So we&#x27;re gonna have to go ahead and apply the chain rule right here. Structurally, we have the tangents of ex inside of a squared function. So we&#x27;re gonna have to first do the squared. I&#x27;m using the power rule. So the two drops down and then we keep what the input waas. And then we need to multiply it by the inside of the function, which is that tan X and derivative of the tangent Is the C camp squared so altogether the derivative is to 10 x c can&#x27;t squared X.

Amrita Bhasin · Answer

this question asked us to find the derivative of seeking squared of acts plus changing squared of axe. We know we&#x27;re gonna be using the power rule and the change rule. So why prime the derivative? We know we have to seek and acts and then the derivative is seeking acts. 10 of X. That&#x27;s the derivative of secret plus 2 10 of x times the derivative of tan, which is seeking squared of acts. This simplifies to four seek it squared of acts times 10 of axe

Jade Meyer · Answer

So we want to find the derivative of tan of X squared y equals X plus y cute. Somewhere to do this, we need to remember that each derivative off 10 of a function you is equal to she can&#x27;t square you times you crime. And we also need to remember the product rule which states that if you&#x27;re finding the derivative of f times G, then that will be a front G plus g prime f great. So now we can solve this problem. So we get well. In this case, the U is expert Why? So we get she can&#x27;t squared of x squared. Why times the derivative of expert times? Why, which would be to X? Why plus x squared y prime. And for that we&#x27;re just using what I ruin. Green over here is equal to x plus y cubed, so that would be three times x plus y. And this is the power rule which states you can just take the coat. The exponents make it the coefficient. Subtract one from the exponents and the multiplied by whatever&#x27;s inside by the derivative, what&#x27;s inside the prophecies. So we have three times x plus y squared times The derivative of X is one plus Why crying? Great. So now what we want to do is figure out a way to isolate Eifert on a wide front. So in order to do this, we should multiply everything up. So we get two x y c can&#x27;t squared X squared Why plus why crime times x squared She can&#x27;t squared X squared y equals three times x plus y squared. In case that didn&#x27;t look enough like a two, I tried to fix it every times x plus y squared Plus why prying times three times x plus y squared Now we want to do is move is bring all the wide crimes to one side and factor it out so we can do both steps at the same time. So we get to X y she can&#x27;t squared of x word y minus three x plus Why squared? Actually, you know what? Let&#x27;s switch the sides just make things easier. So we get why crime times and I&#x27;m factoring things out. Ah, wall moving things to the other side. So we&#x27;re gonna move this over here onto this side we get why prime times why prime times x squared. She can swear of Expert Why minus three times X plus y squared equals three times X plus y squared minus two x y she can&#x27;t squared Expert Why So Now we can isolate. Why prime? So we can say why prime equals and we&#x27;re just dividing both sides by what&#x27;s in the parentheses. Over here. So we get why prime equals three times X plus y squared minus to X y She can&#x27;t squared of X squared y over ex squares. He can&#x27;t swear it of excel of expert Why minus three times x plus y squared and that is our answer.

Sid Wan · Answer

number twelve. Why was hands Axl racks? Month one of this party just meters off records are former Neritan Jax. Pride because sick X fraud eso used corduroy xmas one square to attend X prime circuit Next square. What? Black Swan Swan. So Frank. Ten. That&#x27;s him.

Sid Wan · Answer

Columbia, twenty. Why goes Lancelot ofthe tent square? That&#x27;s absolutely where you live. Peron equals so natural love of something. The one hours after. But fly this car derivatives, which channel and you use general again to attend acts? What clock? Derivative ofthe tent exits back X square. And you can&#x27;t cross one of those two seconds. That&#x27;s where forward ten looks.

Problem

Find the derivatives of the given functions. $$y=…

Problem 33 Easy Difficulty

Find the derivatives of the given functions.
$$2 \tan ^{-1} y+x^{2}=3 x$$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus