find-the-derivatives-of-the-given-functions-ysin-1-x-sqrt1-x2-3

Question

Find the derivatives of the given functions.
$$y=\sin ^{-1} x-\sqrt{1-x^{2}}$$

Tyler Moulton · Accepted Answer

uh huh. We want to find the derivative dy dx for the function. Why is equal to the arc sine of x minus the square root of one minus x square. To solve this problem, we need to rely on differentiation shortcuts. We picked up through a single variable calculus in addition to the inverse trig derivatives, we recently learned. So we have the three major industry directors listed here for this problem. We need to use the fact that DDS arc sine X equals 1/1 minus x square. We also need to use the chain rule for the term route one minus X square. Specifically, we can rewrite what I asked. Arc sine X minus one minus X squared because also right route one minus X squared as one minus X squared, which is the power of one half. So we can proceed now to take the derivative dust. Dy dx is 1/1 minus X squared. This is the river of arc sine X minus negative two X over to root, woman is X squared. This is the derivative of route one minus X squared, taking the chain rule. Thus combining our denominators, we have solution DY dx equals two minus two X over to route one minus X squared.

Madi Sousa · Answer

in this problem. We are practicing our differentiation skills specifically with using inverse triggered a metric functions. And also, this is a great example of in very informal proof. And this is a great precursor to future math. Classes that you might take were given the function y equals x times, the inverse sign of X plus the square root of one minus X squared. So we have to differentiate this to prove that we get the inverse sign of X. We&#x27;re told that&#x27;s what we have to wind up with. So why prime are derivative would be equal to the derivative with respect to X of X sine inverse X plus the derivative of the square root of one minus X squared. So how am I going to do this? Well, this first term looks like a product, so we&#x27;re going to use the product rule and the second term we&#x27;re going to use chain rule. So when we apply, those rules will get that Why prime equals the inverse sign of X times one plus x times one over the square root of one minus X squared, plus 1/2 times the square root of one minus X squared times negative two x So hopefully that made sense how we went from product ruled chain rule to get this derivative here. And then we could simplify it. We could get why prime equals the inverse sign of X plus X over the square root of one minus X squared minus X over the square root of one minus X squared. While these two terms are the exact staying with opposite signs so they can cancel. So we&#x27;re going to get that. Why Prime equals the inverse sign of X, just as we were supposed to. The problem tells us that that&#x27;s what we have to find. So I hope that this problem helped you understand a little bit more about differentiation, how we can choose the rules to differentiate. And then I hope this helped you understand a little bit more about about an informal proof, or maybe what to do when a problem tells you to prove something

Ernest Castorena · Answer

function and let&#x27;s see, we&#x27;re gonna do product will first. So we&#x27;re gonna have sine inverse of X and then the other factor her term will be Let&#x27;s see X over the square root of one minus expert. Not that, and ah, the derivative of the last term and original function will be negative one x by general, over the square root of one minus x squared All these kinds allow and we actually just get are a sign of X.

Amy Jiang · Answer

Okay, so let&#x27;s start by finding a crime about So we see you that for our first term, we have X Times singer Vex facilities are product little, starting with the derivative of X that gives this one times are remaining term and then plus the derivative of singe, which is that&#x27;s kohsh of X. Times are remaining term that&#x27;s X and then minus deserve a tip of kosher vex, which is singer Vex. And we see that we have these two terms that can be cancelled and we&#x27;re left with f prime about that&#x27;s equal to X times kosher.

Linh Vu · Answer

and this question, You&#x27;ve been a function why he called you ex Tim. Sign egos of the ANC&#x27;s plus square it under one minutes. Next square and question asked her to find a y prime. And the first time we see them, we have to be used for this first term. Here we had your planner product who, because we had your function. Yeah, on recording. And we have a duty m sway the derivative with a coach it a new primping plus the premise you and then finally can be. But you&#x27;re right. That is, uh, experience them. Sigh inverse of x plus x temps. I inverse and the eggs really do. And for the second term here we can rewrite the square root into the power. So I will present. It&#x27;s about 1/2. And then we were able job, Lina Power formula so much in the Echo two plus have off the one minus x square. Then we terms with by general when it you&#x27;re crying the minus X square derivative. And now there are several things. When did you do with Now only the terms have entered the river to have to continue here. So we can do underside first for the X derivative. Could you want us? Very obvious now for the Cy inverse off exterior. But if we know by formula, we get it. Could you won over square root of the one minus x square and understand for that. And now for no one minus x square, The relative the virility of one. It could you zero. And that the Riverdale, the Manus X squared equal to minus two x. So have three of them. So we should be about him looking now. So I left on my primary coaching position. Mechanical Jew one. So we would be saying goes on the X plus. Thanks. Attempts for this one. We get to go to this so we can raise time as the fraction. Now be next. Dividing by square pretender One minus X square now, plus Ah, 1/2 off us. One minus thanks. Square times with Ah, I must two x near. So we will have. This will have a larger boat. Doesn&#x27;t be about off. The man has going out through the management of Jew and temple. The man is two X. We can run this now into the new form will be. We have the two here Comes along with this to you. So eventually would have my enough Thanks over one minus x squared in the denominator about a square root beer And they will say this one and this one their exam. It is something so it can consume them. And then we have left with only wear Pamlico jealous I enclose of X, and that would be the answer.

Theresa Nguyen · Answer

the first thing we&#x27;re going to do to solve For wise people to wound over two plus sign of X is to use the exploded role. One over a is equal to a to the negative one. This will look like the over DX of two plus side of X to the negative one. Now we&#x27;re going to use the chain rule to find this derivative d f of you over de X is equal to d f over de you multiplied by D you over de X In this instance R f is you to the negative one while are you is two plus sign of X But together our new derivative will look like d over D you of you to the negative one multiplied by D over DX of two class side of X. Now we&#x27;re going to look for the derivatives of D u and D X de over the u of u two. The negative one can be found using the Powerball D over DX of X to the A is equal to a times X to the A minus one. Here are a is negative one and her d x is d you so put together, it will look like so negative one times you to the negative one minus one which is also negative one times you to the negative too, which is also negative. One over you squared. This is our d&#x27;you Now we&#x27;re looking for r D x D over DX of two plus sign of X. This could be found using these some difference Rule F plus minus G prime is equal Teoh F prime plus minus G time. This will be equal to D over DX up to plus D over DX of sign of X. So the over DX of two is equal to zero. The over the X of sign of X is equal to co side effects. Now that we know our do you and D X, let&#x27;s put them all together we will get negative one over you squared, multiplied by coastline of acts which will look like negative close side of X with the you replace with the other values to plus sign of X. All of this is squared. This is the final answer

Problem

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

Problem 30 Easy Difficulty

Find the derivatives of the given functions.
$$y=\sin ^{-1} x-\sqrt{1-x^{2}}$$

Answer

$\frac{d y}{d x}=\frac{1+x}{\sqrt{1-x^{2}}}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Samuel H.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{d y}{d x}=\frac{1+x}{\sqrt{1-x^{2}}}$

Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Samuel H.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Grace H.

Anna Marie V.

Samuel H.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus