【正确答案】 1、{{*HTML*}}(x-y)e^xy(2-x²-y²)    

【答案解析】令x+y=u，x-y=v，则f(u，v)=(a²+v²)e^uv
f(x，y)=(x²+y²)e^xy
f'_x(x，y)-f'_y(x，y)=2xe^xy+y(x²+y²)e^xy一2ye^xy-x(x²+y²)e^xy
=(x-y)e^xy(2-x²-y²)