My task is to find derivative of

\(\displaystyle (\ln x)^x\)

so I got

\(\displaystyle (\ln x)^x \cdot(\ln(\ln x)+ \frac{1}{\ln(x)})\)

but in textbook it is simplified to

\(\displaystyle (\ln x)^x \cdot(\ln(x) +1)\)

my qouestion: could anyone show me steps to get \(\displaystyle \ln(x) +\)1 from previous step?

Edit: 1 more question:

(x^x)' was also simplified to x^x (ln x +1)

where does that +1 come from again?