It's not correct.
Write
Now, compute
I'm trying to understand what you did there, but I also have a second method,
Which is: lny = xln(lnx)
Would this also be correct?
So...
y'/y = ln(lnx) + x * 1/lnx * 1/x
y' = y(ln(lnx) + 1/lnx)
y' = (lnx)^x(ln(lnx) + 1/lnx)
Or is this also wrong?