设Z=e^xy COS(xy),求dz|(0,1)

问题描述:

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