Differentiation

$\quad x^{\left(x^x\right)}\left(x^x+1+\log x\right)$

$x^{\left(x^x\right)}\left(x^x+\log x\right)$

$x^{\left(x^x\right)}\left(x^x+x^{x-1} \log x(1+\log x)\right)$

$\quad x^{\left(x^x\right)}\left(x^{x-1}+x^x \log x(1+\log x)\right)$