问题
填空题
设
,则f’x(x,y)-f’y(x,y)=______.
答案
参考答案:(x-y)exy(2-x2-y2)
解析:令x+y=u,x-y=v,则f(u,v)=(a2+v2)euv
f(x,y)=(x2+y2)exy
f’x(x,y)-f’y(x,y)=2xexy+y(x2+y2)exy一2yexy-x(x2+y2)exy
=(x-y)exy(2-x2-y2)
设
,则f’x(x,y)-f’y(x,y)=______.
参考答案:(x-y)exy(2-x2-y2)
解析:令x+y=u,x-y=v,则f(u,v)=(a2+v2)euv
f(x,y)=(x2+y2)exy
f’x(x,y)-f’y(x,y)=2xexy+y(x2+y2)exy一2yexy-x(x2+y2)exy
=(x-y)exy(2-x2-y2)