Question

设z=f(xy,x-y),其中f具有二阶连续偏导数,求(əz^2)/(əxəy)

Answer 1

əz/əy=xf1(xy,x-y)-f2(xy,x-y)

a^2z/(əxəy)=ə(əz/əy)/əx

=f1(xy,x-y)+x(yf11(xy.x-y)+f12(xy,x-y))-yf21(xy,x-y)-f22(xy,x-y)

=f1(xy,x-y)+xyf11(xy,x-y)+xf12(xy,x-y)-yf21(xy,x-y)-f22(xy,x-y)