x = yln(xy)dx = d(yln(xy)) = ln(xy)dy + (y/(xy))d(xy) = ln(xy)dy + (1/x)(ydx + xdy) = ln(xy)dy + (y/x)dx + dy合并同类项有(ln(xy) + 1)dy = (1 - y/x)dxdy/dx = (x - y)/(xln(xy) + x)可是最后的答案是：(xy-y^2)/(xy+x^2)将原式子的ln(xy)=x/y代入最后的导数表达式就可以了。