Question

设函数z=x+y/x-y 则dz=?

Answer 1

f(x)=z=x+y/x-y

dz=fxdx+fydy=[[(x-y)-(x+y)]/(x-y)^2 ]dx+[[(x-y)+(x+y)]/(x-y)^2]dy

=-2y/(x-y)^2 dx+2x/(x-y)^2 dy

=2/(x-y)^2 (xdy-ydx)