1、设z=f（u,v）,而u=x^2+y,v=sinx-y,求,,dz.

1
dz=f'(u)du+f'(v)dv
=f'(u)*(2x*dx+dy)+f'(v)*(cosx*dx-dy)
=[2x*f'(u)+f'(v)*cosx]dx+[f'(u)-f'(v)]dy
z'(x)=2x*f'(u)+f'(v)*cosx
z'(y)=f'(u)-f'(v)
其中f'(u)是指f(u,v)对u的偏导……
2
dz=(ydx+xdy)*e^(x+y)+xy*e^(x+y)(dx+dy)
=(y+xy)*e^(x+y)dx+(x+xy)*e^(x+y)dy
z'(x)=(y+xy)*e^(x+y)
z'(y)=(x+xy)*e^(x+y)