Question

设u=xsin2y+y^2z+e^(xy),求du

Answer 1

u=u(x,y,z)=xsin(2y)+y^(2z)+e^(xy)

∂u/∂x=sin(2y)+ye^(xy)

∂u/∂y=x+2zy^(2z-1)+xe^(xy)

∂u/∂z=2 lny y^(2z)

du=[sin(2y)+ye^(xy)]dx + [x+2zy^(2z-1)+xe^(xy)]dy + 2 lny y^(2z)dz