Z=e^x+y复合函数求导

z=e(x+y)
x+y=u u'x=(1+y') u'y=x'+1
z=e^u
z'x=u'xe^u=(1+y')e^(x+y)
z'y=u'ye^u=(x'+1)e^(x+y)
dz=(1+dy/dx)e^(x+y) *dx +(1+dx/dy)*e^(x+y)dy
再问： e^xy+y^3-5x=0请问怎么解呢
再答： e^xy=5x-y^3 (xy)'e^xy=5-3y^2*y' (y+xy')e^xy=5-3y^2y' (xe^xy+3y^2)y'=5-ye^xy y'=(5-e^xy)/(xe^xy+3y^2)