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.

Think of $x$ as a function of two variables $z$ and $w$. Then $x(z,w)=w$. Since $z$ doesn't appear in this expression, you have $\partial x/\partial z = 0$.
The point is to express $x$ and $y$ as functions of $z$ and $w$. Then regarding $x$ and $y$ as the dependent variables, and $z$ and $w$ as the independent variables, compute the partials $\tfrac{\partial}{\partial z}$ and $\tfrac{\partial}{\partial w}$ of $x=x(z,w)$ and of $y=y(z,w)$.
