求二阶偏导数
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求二阶偏导数
对方程两端求微分,得
y²z³dx+2xyz³dy+3xy²z²dz-5(zdx+xdz)-(y²dx+2xydy) = 0,
整理,得
dz = [(y²z³-5z-y²)/(3xy²z²-5x)]dx+[(2xyz³-2xy)/(3xy²z²-5x)]dy;
于是,
Dz/Dx = (y²z³-5z-y²)/(3xy²z²-5x),
Dz/Dy = 2y(z³-1)/(3y²z²-5),
这样,
D²z/Dx² = D(Dz/Dx)/Dx
= D[(y²z³-5z-y²)/(3xy²z²-5x)]/Dx
= …….