find the approximate change in z when the point (x,y) changes from (1,1)to (1.01, 0.90)

Question

f(x,y) = xe^(-y) + ye^(-x)

Answer 1

just use the total differential

dz = Zx dx + Zy dy
= (e^-y - ye^-x)dx + (-xe^-y + e^-x)dy
= (e^-1 - 1e^-1)(.01) + (-1e^-1 + e^-1)(-.1)
= 0

seems odd, but I don't see where I might have gone astray.