given $f$ - a smooth function, $f\colon\mathbb{R}^2\to \mathbb{R}$.
I have a differential operator that takes $f$ to $\frac{\partial f}{\partial x}x$, but I am unsure what this is.
If, for example, the operator tooked $f$ to $\frac{\partial f}{\partial x}$ then I understand that this operator derives by $x$, $\frac{\partial f}{\partial x}x$ derives by $x$ and then what ?
Can someone please help with this ? (I'm confused...)