12.[单选题]设z=f(x,y)其中x=x(u,v)y=y(u,v)且(partial x)/(partial u)=2,(partial y)/(partial u)=3,(partial f)/(partial x)=4,(partial f)/(partial y)=5,则(partial z)/(partial u)的值是多少?

为了求解 $\frac{\partial z}{\partial u}$，我们需要使用链式法则。链式法则在偏导数中的应用可以表示为： \[ \frac{\partial z}{\partial u} = \frac{\partial z}{\partial x} \cdot \frac{\partial x}{\partial u} + \frac{\partial z}{\partial y} \cdot \frac{\partial y}{\partial u} \] 在本题中， $z = f(x, y)$，其中 $x = x(u, v)$ 和 $y = y(u, v)$。根据题目给出的条件，我们有： \[ \frac{\partial x}{\partial u} = 2, \quad \frac{\partial y}{\partial u} = 3, \quad \frac{\partial f}{\partial x} = 4, \quad \frac{\partial f}{\partial y} = 5 \] 将这些值代入链式法则的公式中，我们得到： \[ \frac{\partial z}{\partial u} = \frac{\partial f}{\partial x} \cdot \frac{\partial x}{\partial u} + \frac{\partial f}{\partial y} \cdot \frac{\partial y}{\partial u} \] \[ \frac{\partial z}{\partial u} = 4 \cdot 2 + 5 \cdot 3 \] \[ \frac{\partial z}{\partial u} = 8 + 15 \] \[ \frac{\partial z}{\partial u} = 23 \] 因此， $\frac{\partial z}{\partial u}$ 的值是 $\boxed{23}$。