Question

复合函数的偏导数 第一个和第三个

Answer 1

1）Dz/Dx = (Dz/Du)(Du/Dx)+(Dz/Dv)(Dv/Dx) = (2u)*1+(2v)*1 = ……,

Dz/Dy = (Dz/Du)(Du/Dy)+(Dz/Dv)(Dv/Dy) = (2u)*1+(2v)*(-1) = …….

2）取对数,得

ln|z| = ln(x²+y²)-ln|x|-ln|y|+[(x²+y²)/xy],

求微分,得

dz/z = [1/(x²+y²)]*(2xdx+2ydy)-dx/x-dy/y+[(2xdx+2ydy)*(xy)-(x²+y²)(ydx+xdy)]/(xy)²,

整理成

dz = -------dx+-------dy

的形式,即得

Dz/Dx = ……,

Dz/Dy = …….