find-y-in-terms-of-x-fracd-yd-x6-x2-curve-passes-through-02-2

Question

Find $y$ in terms of $x$.
$\frac{d y}{d x}=6 x^{2},$ curve passes through (0,2)

Dwijendra Rao · Accepted Answer

Hello. We have to find why in terms of eggs. It is given that in the question do you ever dx? He comes to six X. Squared and the car passes through the park. Zero comma two. Okay. Should be very close to six x square Dx. So we were indicated. So this will be a cost to six x cure boundary. This constancy and discourage passes through the point zero comma to so. Mhm. So this point will satisfy the the situation zero comma two satisfied the equation of car so we can add to it cost too zero Plus C. So that will be costas sequence to book to the car vacation by costume two of x. q plus see that means he is too. So this is the question of the car. I hope you understood. Thank you.

Amrita Bhasin · Answer

this question asked us for the equation of the curve that passes through the 0.0 or two and his slope X y is X over. Why? Okay, now what we know is that given the fact that we have a slope at acts over why this means that D y o ver de acts this is slope notation in this problem can be written as equal to X over. Why now? We want all the white terms on the left hand side. So we&#x27;re just gonna rearrange this and then all the ex terms on the right hand side because now we can We&#x27;re easily integrate. Increased the expo number one divide by the new exponents. Now, how why Squared is X squared plus two c not substituting X&#x27;s here, wise to we know we now need to solve for C so we should get C equals and we end up with C equals two. Okay, Now substitute this about this value back into our equation plus two c So, plus two times two when they get why squared is X squared plus four. Now remember, we don&#x27;t want y squared equals. We want y equals We must take the square root. Now notice how it should be positive or negative or plus or minus because we&#x27;re doing the square root. However, remember why zero is, too, Which means this has to be positive, which means be just disregard the negative solutions. So this is the answer.

Nick Johnson · Answer

Okay, so here is given that the slope. So the slope is do I d axe derivative. So the slow, um, off the curve. Right. E x is, um so you are. The X is well, is negative. X over four. Why? Okay, so we can rewrite the differential equation as well as four. Why de y is equal, Teoh. Negative x dx. Okay, so separate are very moles. Get X rays on one side, wise and the other, um And then we have a differential equation in separate form so that we can integrate both sides to integrate left side and we integrate the right side. Okay, so what we get here while the in agro of four Y de y That&#x27;s just, um, four y squared over two, which is two. Why squared is equal to, Well, negative X squared. Negative X square over two. And then plus our constant c. Okay, um, So what we get here is where all that d y I&#x27;m sorry to Why square plus X squared over two is equal to see right? So we can then replace X with zero. And why, with 1/2 right, given the point that were given him and then south for C. So we get to times Well, 1/2 squared, plus Well, zero squared over to what you just plus zero is equal to see. So we get, um, 1/2 square. Um, times two, which is just 1/2. Right. So 1/2 is he going to see someone? Half is equal to see. Okay, then weaken Substituted 1/2 in for C in two y squared, plus X squared over two equal c. And we get to why square plus X squared over shoe is equal to Well, you could 1/2. Okay, so, um well, this implies that, um, the fractions office supplies that. Let&#x27;s see Exc Well, but that&#x27;s a first X squared plus four. Why? Square is equal to one. Cancel therefore the equation of the curve we&#x27;re looking for. There it is. Right. So we get the prayers of the curve is X squared plus four X is equal to one. This is X where our X squared plus four y square is equal to one. All right,

Cory Kuzinski · Answer

Michael&#x27;s X squared is kind of our parent function. That kind of it is if we want to do a translation. Six years, right. And what we&#x27;re gonna do is we&#x27;re gonna take that X value, and we&#x27;re going to subtract six. So that would be a translation. Six units to the right to put a box around it has our answer.

Sriram Soundarrajan · Answer

today we&#x27;re going to start probable 69. Not to give. Immigration is like at the square equals minus six. Right? And for intelligent one like my six commenters, if we have to find the equation all the dancing But this girl so first, find a slow But this girl, it is like two x is a good of minus six. Do you like about sex for divided by the X, we&#x27;ll be getting its leg by enough to work for basics. My enough to works by six. So the pine mind I think about my nothing for the regret leg. Ah, think through window might have through into minus six by six year Gate two. Okay, Now, when you divine the aggression off the Bandon with flow it cause too at bottles through the point of minus four minus six. Why my enough. Minus six, thereby eggs minus minus 50. Which is a photo. Who so you don&#x27;t be like by plus 60 quarter to express too well by Easy Guardo. Two legs plus six. Thank you.

Will Erickson · Answer

Hi there. On this problem, we are asked to find the derivative D Y d x at a certain point for an equation. So let&#x27;s write the equation first were asked to find the derivative given this equation X plus two all squared minus six times. Go on to live plus three. All squared equals three and her point. Well, keep up here in the upper right just so we don&#x27;t forget what it is. Our point that will end up taking the derivative at will be one minus one. Okay, As always, let us take the derivative of both sides with respect to X and see what we get. So on the left, the derivative off X plus two quantity squared. We&#x27;ll have to use the chain rule technically, with the little end up not making too much of a difference, right? But the derivative of that is two times X plus two and to the first power and then times the derivative of X plus two. But the derivative of X plus two is just one. So that first term, all this end up two times exposed to. But don&#x27;t forget, we should always think of using the chain rule, even if it ends up not affecting the results here. And the second case, the derivative of six times to A to Y plus three, all squared. Same thing. We should think of the train room so we&#x27;ll end up with Ah, so this thank you. 12 cents this two ends of being multiplied in front by the chain rule and to ah, plus three at all of the first. Now that&#x27;s where the general is important. We need to multiply by this derivative that&#x27;s in the parentheses. The derivative of two y plus three is too, but mean to multiply by Y prime. For all these problems, y is a function of X. So when we take a derivative of why be multiplied by white prime. So that is the left side, Theo right side. The derivative of three is just zero. So that&#x27;s a little easier. And now we have to do is get wide prime by itself. So we will start when we subtract this term from both sides, meaning we will have that on the right and on the left, we can clean this up a little bit. We have minus 12 times two that&#x27;s negative. 24 times to Iive, plus three times why prime and remember, the goal is always to get that white prime by itself. So now we can just divide both sides by that red stuff. There, you&#x27;ll end up with y Prime equals negative two times exposed to all over. Most rewrite that left side minus 24 to why plus three one is will simplify a little bit. That negative too in the negative 24. Well, this come down to one over 12. Good. We don&#x27;t have to clean it up too much because our goal is just a plug in this point and get a number at the very end. So this just means we&#x27;re gonna set X equals the one. Why equal to minus one? In other words, that the derivative at the 0.1 minus one equals. So let&#x27;s see. We&#x27;ll plug in the one for X and we will plug in negative one for why see what we get on the top one plus two plus three on the bottom. So in the parentheses, two times negative one is negative. Two plus three is one so three over 12 or 1/4 and that is our final answer. Hopefully, that helped

Problem

Find $y$ in terms of $x$. $\frac{d y}{d x}=8 x+1,…

Problem 37 Easy Difficulty

Find $y$ in terms of $x$.
$\frac{d y}{d x}=6 x^{2},$ curve passes through (0,2)

Answer

$y=2 x^{3}+2$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Kayleah T.

Caleb E.

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Precalculus Review - Intro

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$y=2 x^{3}+2$

Basic Technical Mathematics with Calculus

Heather Z.

Kayleah T.

Caleb E.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Heather Z.

Kayleah T.

Caleb E.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus