I am looking for a general formula for $$D_n=\frac{d^n}{dx^n}x^x$$ Here's what I've gotten so far:
$n=0$: $$D_0=x^x$$ $n=1$: $$D_1=x^x(\log x+1)$$ $n=2$: $$D_2=x^{x-1}+x^x(1+2\log x+\log^2 x)$$ And then I gave up. But I would be surprised if there wasn't a general formula.
In any case, I am trying to find $D_n$ so that I can create a Taylor series for $x^x$. If this isn't the way to go, please point me in the right direction or give me a series representation for $x^x$
