How is it that this partial derivative is equal to 0? In my probability textbook are the following equations:
$Z=X/Y$ and $X=W$.
There is a Jacobian as follows: 
$$J =
\begin{bmatrix}
  \frac{\partial x}{\partial z} & 
    \frac{\partial x}{\partial w} \\[1ex] % <-- 1ex more space between rows of matrix
  \frac{\partial y}{\partial z} & 
    \frac{\partial y}{\partial w} \\[1ex]
\end{bmatrix}$$
solving for the partial derivatives (according to my textbook):
$$J =
\begin{bmatrix}
  0 & 
    1 \\[1ex] % <-- 1ex more space between rows of matrix
  -\frac{w}{z^2} & 
    \frac{1}{z} \\[1ex]
\end{bmatrix}$$
How is it that $\frac{\partial x}{\partial z} = 0?$ 
My thinking is $X=YZ$ so $\frac{\partial x}{\partial z} = Y$. Where am I going wrong? All the other partial derivatives make perfect sense to me.

Thanks in advance.

The Jacobean concerns $x,y$ as functions of $z,w.$
So the equations to work with are $x=w$ and $y=\frac{w}z.$
