21.简答题设函数z=z(x,y)方程 4x^2+3y^2+2z^2=1确定，求dz.

设 $F(x, y, z) = 4x^2 + 3y^2 + 2z^2 - 1$，则 \[ F_x = 8x, \quad F_y = 6y, \quad F_z = 4z. \] 由隐函数的偏导数公式得 \[ \frac{\partial z}{\partial x} = -\frac{F_x}{F_z} = -\frac{8x}{4z} = -\frac{2x}{z}, \] \[ \frac{\partial z}{\partial y} = -\frac{F_y}{F_z} = -\frac{6y}{4z} = -\frac{3y}{2z}. \] 全微分 $dz$ 为 \[ dz = \frac{\partial z}{\partial x}dx + \frac{\partial z}{\partial y}dy = -\frac{2x}{z}dx - \frac{3y}{2z}dy. \] **答案：** \[ \boxed{-\frac{2x}{z}dx - \frac{3y}{2z}dy} \]