根据隐函数求导公式，可以得到：
$\frac{\partial z}{\partial x} = -\frac{yz\cos(xyz)}{xy^2z\cos(xyz)-z^2x\cos(xyz)} = -\frac{y\cos(xyz)}{xy\cos(xyz)-z\cos(xyz)}$
$\frac{\partial z}{\partial y} = -\frac{x\cos(xyz)}{xy^2\cos(xyz)-z^2y\cos(xyz)} = -\frac{x\cos(xyz)}{xy\cos(xyz)-z\cos(xyz)}$
根据全微分的定义，有：
$d(z) = \frac{\partial z}{\partial x}dx + \frac{\partial z}{\partial y}dy$
令$t = xyz$，则有：
$dt = (yzdx + xzdy) + (xydz)$
因此，
$dz = \frac{1}{x^2y^2}\left[(yzdx + xzdy) + (xydz)\right]$
$= \frac{y^2zdx + x^2zdy + xydz}{x^2y^2}$
根据题目所求，有：
$\frac{(OZ)}{3oz} = \frac{\partial z}{\partial x} \cdot \frac{\partial^2 t}{\partial x^2} + 2 \frac{\partial z}{\partial x} \cdot \frac{\partial^2 t}{\partial x \partial y} + \frac{\partial z}{\partial y} \cdot \frac{\partial^2 t}{\partial y^2}$
其中，
$\frac{\partial^2 t}{\partial x^2} = y^2z\sin(xyz) - 2yz^2\cos(xyz) - xz\sin(xyz)$
$\frac{\partial^2 t}{\partial y^2} = x^2z\sin(xyz) - 2xz^2\cos(xyz) - yz\sin(xyz)$
$\frac{\partial^2 t}{\partial x \partial y} = z^2\cos(xyz) - xy\cos(xyz)$
代入上面求得的$\frac{\partial z}{\partial x}$和$\frac{\partial z}{\partial y}$，并化简可得：
$\frac{(OZ)}{3oz} = -\frac{1}{x^2y^2}\left[(y^3z^2\cos(xyz) - 3xyz^3\cos(xyz) + x^2yz\sin(xyz))\frac{\partial z}{\partial x} + (x^3z^2\cos(xyz) - 3xyz^3\cos(xyz) + y^2xz\sin(xyz))\frac{\partial z}{\partial y}\right]$
代入上面求得的$\frac{\partial z}{\partial x}$和$\frac{\partial z}{\partial y}$的式子，整理可得：
$\frac{(OZ)}{3oz} = -\frac{z\cos(xyz)}{3xy\cos(xyz) - 3z\cos(xyz)}$
因此，$\frac{(OZ)}{3oz}$的值可以根据$x$和$y$的值以及$x,y$对应的$z$值来计算。
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