设Z=e^xy COS(xy),求dz|(0,1)

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设Z=e^xy COS(xy),求dz|(0,1)
设Z=e^xy COS(xy),求dz|(0,1)

设Z=e^xy COS(xy),求dz|(0,1)
dZ = эZ/эx *dx + эz/эy*dy
= y*e^(xy)*cos(xy)*dx + e^(xy)*[-ysin(xy)]*dx
+ x*e^(xy)*cos(xy)*dy + e^(xy)*[-xsin(xy)*dy
dZ|(0,1) = 1*e^0*cos0*dx - e^0*y*sin0*dx +0*e^0*cos0*dy - e^0*0*sin0*dy
= dx

z=e^xycosxy
z'x=(1+y')e^xycosxy-(1+y')e^xysinxy
z'y=(1+x')e^xycosxy-(1+x')e^xysinxy
dz=z'x dx+z'ydy
dz|(0,1)=(1+y')dx+(1+x')dy
=dx+(dy/dx)dx+(1+dx/dy)dy
=2dx+2dy

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