设F(x，y)=
{y(3x2-y2)/(x2+y2)-2x2y-(x2-y2)/(x2+y2)2，x2+y2≠0
{0，x2+y2=0
G(x，y)=
{x(x2-3y2)/(x2+y2)-2xy2(x2-y2)/(x2+y2)2，x2+y2≠0
{0，x2+y2=0
求Fy(0，0)及Gx(0，0)．
根琚定义 Fy(0，0)=limΔy→0[F(0，0+Δy)-F(0，0)]/Δy=limΔy→0{[Δy(0-Δy2)/(0+Δy2)]-0}/Δy =limΔy→0-Δy3/Δy3=-1 Gx(0，0)=limΔx→0[G(0+Δx，0)-G(0，0)]/Δx=limΔx→0Δx/Δx=1
