Problem with a taylor serie expansion

[Amaelle]

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 f_xy I got
f_xy=xye^xy
f(0,1)=0 so x(y-1) should not appear in the solution
am I wrong?

thank you!

 

[FactChecker]

I can't see the attachments.

 

[Amaelle]

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