例7.4.9利用全微分形式不变性解例7.4.1 解：dz=d(e"sinv) e"sin vdu +e"cosvdv =e*[sin(x+y)d(xy)+cos(x+y)d(x+y)] =ex[sin(x+y)(ydx+xdy)+cos(+)(dx+dy)] =ex[ysin(x+y)+cos(x+y)]dx +e*[xsin(x+y)+cos(+)]dy 所以 8x =ex[y.sin(x+y)+cos(x+) ex[x.sin(x+y)+cos(x+y)] BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS PRESS 返回 结束目录 上页 下页 返回 结束 例1 . z e sin v, u xy, v x y, u     , . y z x z     求 e [sin(x y) cos(x y) ] xy     例7.4.9 利用全微分形式不变性解例7.4.1 解: dz  d( ) v u u  e sin d e [ y sin(x y) cos(x y)] xy     e [ y sin(x y) cos(x y)] x z xy        e [x sin(x y) cos(x y)] y z xy        所以 v u e sin v v u  e cos d e [sin(x y) cos(x y) ] xy   d (xy)   d (x  y) e [xsin(x y) cos(x y)] xy     (dx  dy) d x dy (yd x  xdy)