Define a operation
$(\partial \cdot x)*f(x)=\frac{d(xf(x))}{dx}$
In the notes it has that
$(\partial^n \cdot x)*f(x)=(n \partial^{n-1 }+ x \cdot \partial^n)*f(x)$
Is this wrong? I can't get this
Well, $(\partial^n \cdot x)*f(x)=\frac{d^{n-1}}{dx^{n-1}}(\frac{d(xf(x))}{dx})$
Which, doesn't seem to get that.