Finding all the points (x,y) where $f(x,y)=\sqrt{|x^3y|}$ is differentiable.

I started off with this:

If a function is differentiable then:

$f(x\_0+\Delta x,y\_0+\Delta y)=f(x\_0,y\_0)+\frac {\partial f(x\_0,y\_0)}{\partial x}\Delta x+\frac {\partial f(x\_0,y\_0)}{\partial y}\Delta y+\epsilon\sqrt{\Delta y^2+\Delta x^2}$

So what came to my head would be isolating $\epsilon$, And doing a limit where $\Delta x\to0$,$\Delta y \to 0$ and find when it equals to $0$. But the calculating it seems a bit problematic. Especially one that obsolete value.

Any tips?