If \( y = \dfrac1x \), prove that \( \dfrac{dy}{\sqrt{y^4+1}} + \dfrac{dx}{\sqrt{x^4+1}} = 0 \).

If \( y = \dfrac1x \), prove that \( \dfrac{dy}{\sqrt{y^4+1}} + \dfrac{dx}{\sqrt{x^4+1}} = 0 \).

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TopNewest\( xy = 1\)

\( ydx + xdy = 0 \)

\( \frac{ydx}{\sqrt{x^2 + y^2}} + \frac{xdy}{\sqrt{x^2 + y^2}} = 0 \)

\( \frac{dx}{\sqrt{\frac{x^2}{y^2} + 1}} + \frac{dy}{\sqrt{\frac{y^2}{x^2} + 1}} = 0 \)

\( \frac{dx}{\sqrt{x^4+ 1}} + \frac{dy}{\sqrt{y^4 + 1}} = 0 \) – Siddhartha Srivastava · 1 year, 4 months ago

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@Rishabh Cool, this is what I was looking for, what i wanted was that you proceed purely from the given expression and arrive at the result that you are required to prove and not use the result required and substitute to it a condition derived from the given expression. – Akhilesh Prasad · 1 year, 4 months ago

Thanks man, that was very helpful.Log in to reply

– Rishabh Cool · 1 year, 4 months ago

OK......Log in to reply

– Akhilesh Prasad · 1 year, 4 months ago

I don't know how to thank you always attending my doubts as soon as i post them. I am very grateful to you.Log in to reply

– Rishabh Cool · 1 year, 4 months ago

No problem dude ... :-)Log in to reply

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– Akhilesh Prasad · 1 year, 4 months ago

Shouldn't you be proving it from the relation and not by putting the value of \(dy\) & \(y\), cause wouldn't that just mean that you are using the result to prove the result.Log in to reply

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– Akhilesh Prasad · 1 year, 4 months ago

I was not able to find the words for what i wanted to say lemme try it again. What i am saying is shouldn't you solely use the given expression to prove \( \dfrac{dy}{\sqrt{y^4+1}} + \dfrac{dx}{\sqrt{x^4+1}} = 0 \) and not substitute to it what the expression leads to, to get the proof.Log in to reply