求偏导数 xy（x^2-y^2）/（x^2+y^2）fxy(0,0)fyx(0,0) 求大神给详解

解：
f'x(x,y)
=[(3x²y-y³)(x²+y²)-(x³y-xy³)2x]/(x²+y²)²
=[(x^4)y+4x²y³-(y^5)]/(x²+y²)²
f'x(0,0)
=lim(Δx→