第1个回答 2019-03-28
1
u=u(x,y,z)
∂u/∂x=[(x/y)^(1/z)]/(zx)=u/(zx)
∂u/∂y=-[(x/y)^(1/z)]/(zy)=-u/(zy)
∂u/∂z=-[(x/y)^(1/z)](1/z²)ln(x/y)=-u[ln(x/y)]/z²
u=(x/y)^(1/z)在(1,1,1)u=u(1,1,1)=1
∂u/∂x=1,∂u/∂y=-1,∂u/∂z=0
2
du=(∂u/∂x)dx+(∂u/∂y)dy
∂u/∂x=y[cos(xy)]/[sin(xy)]
∂u/∂y=x[cos(xy)]/[sin(xy)]
du=(ydx+xdy)[cos(xy)]/[sin(xy)]
3
∂z/∂x=e^xsinyf1'+2xf2'
∂²z/∂x∂y=e^xcosyf1'+(e^x)²sinycosyf11''+2ye^xsinyf12''+2xe^xcosyf21''+(4xy)f22''