Find the gradient of $\frac{x}{x-y}$ It seems simple on the face of it, but I cannot figure out how to actually do this. I know that you have to find the partial with respect to $x$ and also with respect to $y$, but that's where I get lost.

$f(x,y)=x/(x-y)$
Just use the definition
$\bigtriangledown f(x,y)=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})$
$\frac{\partial f}{\partial x}=-y/(x-y)^2$
$\frac{\partial f}{\partial y}=x/(x-y)^2$
so
$\bigtriangledown f(x,y)=(-y/(x-y)^2,x/(x-y)^2)$
