Question

怎么求z=(x+y)/(x-y)的全微分

Answer 1

求全微分就是求偏导数
把y看成常数 求偏z/偏x 把x看成常数 求偏z/偏y 这是基本功不用说了吧
然后dz=偏z/偏x *dx+偏z/偏y*dy

Answer 2

z=(x+y)/(x-y)
=1+2y/(x-y)
z'x= -2y/(x-y)^2
z'y=2/(x-y)+2y/(x-y)^2=2x/(x-y)^2

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