2 (1) . u = x^2y^2/(x+y)
u' = [2xy^2(x+y)-x^2y^2]/(x+y)^2 = xy^2(x+2y)/(x+y)^2
u' = [2x^2y(x+y)-x^2y^2]/(x+y)^2 = x^2y(2x+y)/(x+y)^2
xu' + yu' = x^2y^2(3x+3y)/(x+y)^2
= 3x^2y^2/(x+y) = 3u
(2) z = ln(e^x+e^y),
z' = e^x/(e^x+e^y) = 1-e^y/(e^x+e^y),
z' = e^y/(e^x+e^y) = 1-e^x/(e^x+e^y),
z'' = e^ye^x/(e^x+e^y)^2
z'' = e^xe^y/(e^x+e^y)^2
z'' = -e^xe^y/(e^x+e^y)^2
则 z'' z'' - (z'')^2 = 0
