设 z=xyf(y/x),f(u)可导,则xZ'x+yZ'y=?（Z'x表示对x求导）

网友回答

Z'x=-yf'(y/x)y/x^2
xZ'=-y^2f'(y/x)/x
Z'y=xf'(y/x)1/x
yZ'y=yf'(y/x)
xZ'x+yZ'y
=-y^2f'(y/x)/x+yf'(y/x)
=y(x-y)f'(y/x)/x
======以下答案可供参考======
供参考答案1:
z=xyf(y/x)
====>Z'x=(-1/x^2)*y*f(y/x)
Z'y=xf(y/x)
xZ'x+yZ'y
=-y/xf(y/x)+xyf(y/x)