z=x^y
lnz=ylnx
z'x/z=y/x,得z'x=zy/x
z'y/z=lnx, 得z'y=zlnx
dz=z'xdx+z'ydy=z(y/x*dx+lnx*dy)
当x=1, y=4, dx=0.02, dy=0.05时,
z=1^4=1
dz=1*(4/1*0.02+ln1*0.05)=0.08
因此1.02^4.05的近似值为1.08