e^(x+y)sin(x+z)=0 z=z(x+y) 求dz

2025-02-25 10:31:23
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回答1:

e^(x+y)sin(x+z)=0
e^(x+y)dsin(x+z)+ sin(x+z)de^(x+y)=0
e^(x+y).cos(x+z) ( dx +dz) + sin(x+z).e^(x+y).( dx+ dy) =0
e^(x+y).cos(x+z) dz =-sin(x+z).e^(x+y).( dx+ dy) -e^(x+y).cos(x+z) dx
=-e^(x+y). [ sin(x+z)+ cos(x+z)] dx - sin(x+z).e^(x+y). dy
dz = -[ tan(x+z)+ 1]dx - tan(x+z).dy