Operate partial derivative as ratio?

alctel

Suppose [itex]x\in\Re^{m}[/itex], [itex]y\in\Re^{n}[/itex], [itex]A\in\Re^{m\times n}[/itex], and [itex]\frac{\partial x}{\partial y}=A[/itex]

Then is this step correct (operate like a ratio)?
[itex]{\partial x}=A {\partial y}[/itex]