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(

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F_y(0，0)及G_x(0，0)．

根琚定义 F_y(0，0)=lim_Δy→0[F(0，0+Δy)-F(0，0)]/Δy=lim_Δy→0{[Δy(0-Δy²)/(0+Δy²)]-0}/Δy =lim_Δy→0-Δy³/Δy³=-1 G_x(0，0)=lim_Δx→0[G(0+Δx，0)-G(0，0)]/Δx=lim_Δx→0Δx/Δx=1