I can not figure out how to write “find $f(x)$ such that $\frac{df}{dx}$ is equal to the inverse function of $f(x)$”, or $f^{-1}(x)$)
I am not looking for the answer to this problem, just how you would write it in notation with $y^\prime$ and such.
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1$y'=y^{-1}(x)$ same as f notation $f'=f^{-1}$ – user577215664 Feb 07 '20 at 21:24
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1@Isham huh, didn’t know you could do that same thing with $y$s – Snacc Feb 07 '20 at 21:25
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Connor $y'$ is just $\frac {dy}{dx}$ like the $f$ notation you are given Then you also have the composition of functions $y'\circ y(x)=x$ – user577215664 Feb 07 '20 at 21:26
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@zwim: in what sense would this question be a duplicate of that one? – Martin Argerami Feb 07 '20 at 22:30
1 Answers
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The usual notation is ambiguous, unfortunately. It is natural to write $y'=y^{-1} $, but you would have to clarify you are talking about the inverse, since it is also natural to read $y^{-1} $ as $1/y $. It is a little less ambiguous if you write $y'(x)=y^{-1}(x) $.
Martin Argerami
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