考研多元微分数学混合偏导数求导次序问题
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/08/10 07:00:11
考研多元微分数学混合偏导数求导次序问题
![](http://img.wesiedu.com/upload/5/95/5956bc0a64468a84ca23ad23f82a5449.jpg)
![](http://img.wesiedu.com/upload/5/95/5956bc0a64468a84ca23ad23f82a5449.jpg)
![考研多元微分数学混合偏导数求导次序问题](/uploads/image/z/16427674-10-4.jpg?t=%E8%80%83%E7%A0%94%E5%A4%9A%E5%85%83%E5%BE%AE%E5%88%86%E6%95%B0%E5%AD%A6%E6%B7%B7%E5%90%88%E5%81%8F%E5%AF%BC%E6%95%B0%E6%B1%82%E5%AF%BC%E6%AC%A1%E5%BA%8F%E9%97%AE%E9%A2%98)
这一题很烦的.条件改写成
w =xy - z,z = z(x,y),x = (u + v)/2,y = (u - v)/2,
则
Dw/Dv = D(xy - z)/Dv
= (Dx/Dv)*y + x*(Dy/Dv) - (Dz/Dx)*(Dx/Dv) - (Dz/Dy)*(Dy/Dv)
= y/2 - x/2 - (Dz/Dx)/2 + (Dz/Dy)/2
D(Dw/Dv)/Du
= D[y/2 - x/2 - (Dz/Dx)/2 + (Dz/Dy)/2]/Du
= 1/4 - 1/4 - {[D(Dz/Dx)/Dx]/2 + [D(Dz/Dx)/Dy]/2}/2 + {[D(Dz/Dy)/Dx]/2 + [D(Dz/Dy)/Dy]/2}/2
= ……,
同样,
D(Dw/Du)/Dv = ……,(留给你)
注意 z 对 x,y 有连续的偏导数,应有
D(Dz/Dx)/Dy =D(Dz/Dy)/Dx,
比较一下就知道了.
再问: 谢谢码那么多子,辛苦了
w =xy - z,z = z(x,y),x = (u + v)/2,y = (u - v)/2,
则
Dw/Dv = D(xy - z)/Dv
= (Dx/Dv)*y + x*(Dy/Dv) - (Dz/Dx)*(Dx/Dv) - (Dz/Dy)*(Dy/Dv)
= y/2 - x/2 - (Dz/Dx)/2 + (Dz/Dy)/2
D(Dw/Dv)/Du
= D[y/2 - x/2 - (Dz/Dx)/2 + (Dz/Dy)/2]/Du
= 1/4 - 1/4 - {[D(Dz/Dx)/Dx]/2 + [D(Dz/Dx)/Dy]/2}/2 + {[D(Dz/Dy)/Dx]/2 + [D(Dz/Dy)/Dy]/2}/2
= ……,
同样,
D(Dw/Du)/Dv = ……,(留给你)
注意 z 对 x,y 有连续的偏导数,应有
D(Dz/Dx)/Dy =D(Dz/Dy)/Dx,
比较一下就知道了.
再问: 谢谢码那么多子,辛苦了