differentiate y=x^(lnx)

First Consider
lny=ln[x^(lnx)]
lny=(lnx)(lnx)=(lnx)^2
Differentiate w.r.t. x
(1/y)y'=2(lnx)(1/x)
y'=(y)2(lnx)(1/x)
y'=2(lnx)[x^(lnx)]/x
=2(lnx){x^[(lnx)-1]}