Can anyone check if this argument works. I just made up this problem to check if I understand whats going on.(adsbygoogle = window.adsbygoogle || []).push({});

Consider F = xy*e^x + y*e^y = K. I want to see if there is a unique solution.

F_{y}= x*e^x + y*e^y + e^y.

Since we are on the surface x*e^x + y*e^y = K.

So if K >= 0 then F_{y}≠ 0. So given any x we can find a unique y.

Did I understand the theorem correctly?

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# Implicit function Theorem

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