Is (dx²)/(d²y) is acceptable as second derivative?

I have just read about derivative that on higher derivative is [d^(n)y/dx^(n)]=y'(n) and also the inverse function (1/y')=x'

But i am still confuse if it is possible
Math / Science

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d-glitch
d-glitch

From Wikipedia:   https://en.wikipedia.org/wiki/Derivative
The dy/dx notation is from Leibniz.  Note that the y term is usually on top.
The ' (or prime) notation is from Lagrange.  Both notations are in common use.

I don't understand you question about an "inverse function."
Ray Paseur

How is this a PHP question? Are you looking for a code sample in PHP?  Or C++?  Please clarify, thanks.
d-glitch

>> JS
Comments and follow-on questions should be posted here not in personal messages.

We can not see the context for the disagreement between you and your colleague.
What is the specific question that caused the disagreement, and what are the competing answers?

I have already noted that your expression is flipped from the usual form of the 2nd derivative:
(d²y)/(dx²)    <== Why do you think that this form is inadeqauate?
John Sebastian

It is because i want to prove it using the inverse function that dy/dx=1/(dx/dy) and dx/dy=1/(dy/dx)
d-glitch

I still don't see a context.  You have mentioned 2nd derivatives, 1st derivatives, inverse functions, and the reciprocal function (1/x).

I don't see a clear starting point, or a path to any useful result.
BigRat

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d-glitch

The questions remains unclear, but BigRat's answer is comprehensive.
Math / Science

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