设z=sinxy+cos(x+y)则dz=

题目

设z=sinxy+cos(x+y)则dz=
高数题,会做的帮个忙,

答案

dz=d(sinxy)+d(cos(x+y))
=cosxyd(xy)-sin(x+y)d(x+y)
=ycosxydx+xcosxydy-sin(x+y)dx-sin(x+y)dy
=[ycosxy-sin(x+y)]dx+[xcosxy-sin(x+y)]dy