先求函數(shù)的全導數(shù)為：
df(x,y)={[xy(x^2-y^2)]'(x^2+y^2)-xy(x^2-y^2)(x^2+y^2)'}/(x^2+y^2)^2
={[(xy)'(x^2-y^2)+(xy)(x^2-y^2)'](x^2+y^2)-xy(x^2-y^2)(2xdx+2ydy)}/(x^2+y^2)^2
={[(ydx+xdy)(x^2-y^2)+xy(2xdx-2ydy)](x^2+y^2)-2xy(x^2-y^2)(xdx+ydy)}/(x^2+y^2)^2
=【y(x^4-4x^2y^2-y^4)/(x^2+y^2)^2】dx-【x(x^4-5y^4)/(x^2+y^2)^2】dy
前者dx前面的為對x的偏導數(shù),后于dy前面的為對y的偏導數(shù).