Problem with a taylor serie expansion

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The discussion revolves around a problem with a Taylor series expansion, where one participant expresses disagreement with a proposed solution. They calculated the mixed partial derivative fxy as xyexy and noted that f(0,1) equals zero, suggesting that x(y-1) should not be part of the solution. After further interaction, the participant acknowledges a miscalculation on their part, leading to the resolution of the problem. The thread highlights the importance of careful calculation in mathematical solutions. Ultimately, the issue was resolved through clarification and self-correction.
Amaelle
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Homework Statement
Look at the image
Relevant Equations
Tayolr development
Greetings
https://www.physicsforums.com/attachments/295843

I really don´t agree with the solution
https://www.physicsforums.com/attachments/295846

as I calculated fxy I got
fxy=xyexy
f(0,1)=0 so x(y-1) should not appear in the solution
am I wrong?

thank you!
 
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thank you I solved the problem it was my wrong calculation!
 

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