Take the tour ×  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.  share|improve this question What is
the symbol you're defining a meaning for -- is it
"$\partial\cdot$", or "$*$", or what? –  Henning Makholm Nov 27
'11 at 0:13 add comment  1 Answer  up vote 2 down vote accepted
The derivative of $xf$ is $f+xf'$. The 2nd derivative is
$2f'+xf''$. The 3rd derivative is $3f''+xf'''$. This seems to me
to be in accord with the formula in the notes.  share|improve
this answer Lol I feel so stupid. Thanks –  simplicity Nov 27
'11 at 0:19 add comment  Your Answer