求函数z=x^2(siny^2)+2xysinxsiny+y^2的全微分

2025-06-20 13:40:20
推荐回答(1个)
回答1:

Z'x=2xsin(y²)+2ysinxsiny+2xycosxsiny
Z'y=x²*cos(y²)*2y+2xsinxsiny+2xysinxcosy+2y
故sz=Z'xdx+Z'ydy=[2xsin(y²)+2ysinxsiny+2xycosxsiny]dx+[2yx²cos(y²)+2xsinxsiny+2xysinxcosy+2y]dy