/ x\ / x \ / x\
\x / x - 1 |x x | \x / x - 1 /x - 1 \
x *x *|-- + x *(1 + log(x))*log(x)| + x *x *|----- + log(x)|
\x / \ x /
$$x^{x^{x}} x^{x - 1} \left(x^{x} \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{x^{x}}{x}\right) + x^{x^{x}} x^{x - 1} \left(\log{\left(x \right)} + \frac{x - 1}{x}\right)$$
/ -1 + x \
/ x\ | 2 2 - ------ / 2 \ |
\x / -1 + x |/-1 + x \ x x | 1 log(x) x /1 \ 2 2*(1 + log(x))| x /1 \ /-1 + x \|
x *x *||------ + log(x)| + ---------- + x *|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------| + 2*x *|- + (1 + log(x))*log(x)|*|------ + log(x)||
|\ x / x | 2 x \x / x | \x / \ x /|
\ \ x / /
$$x^{x^{x}} x^{x - 1} \left(2 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{x - 1}{x}\right) + x^{x} \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) + \left(\log{\left(x \right)} + \frac{x - 1}{x}\right)^{2} + \frac{2 - \frac{x - 1}{x}}{x}\right)$$
/ 2*(-1 + x) / -1 + x\ /-1 + x \ / -1 + x\ \
/ x\ | 3 / 3 2 \ 3 - ---------- 3*|2 - ------|*|------ + log(x)| | 2 2 - ------| / 2 \|
\x / -1 + x |/-1 + x \ x |2 3 2*x /1 \ 3 log(x) 3*(1 + log(x)) 3*(1 + log(x)) 3*(1 + log(x))*log(x) x /1 \ / 1 log(x) 2 2*(1 + log(x))\| x \ x / \ x / x /1 \ |/-1 + x \ x | x /-1 + x \ | 1 log(x) x /1 \ 2 2*(1 + log(x))||
x *x *||------ + log(x)| + x *|-- + -- + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) - ------ - -------------- + --------------- + --------------------- + 3*x *|- + (1 + log(x))*log(x)|*|- -- + ------ + (1 + log(x)) *log(x) + --------------|| - -------------- + -------------------------------- + 3*x *|- + (1 + log(x))*log(x)|*||------ + log(x)| + ----------| + 3*x *|------ + log(x)|*|- -- + ------ + x *|- + (1 + log(x))*log(x)| + (1 + log(x)) *log(x) + --------------||
|\ x / | 3 2 \x / 2 2 x x \x / | 2 x x || 2 x \x / \\ x / x / \ x / | 2 x \x / x ||
\ \x x x x \ x // x \ x //
$$x^{x^{x}} x^{x - 1} \left(3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\log{\left(x \right)} + \frac{x - 1}{x}\right)^{2} + \frac{2 - \frac{x - 1}{x}}{x}\right) + 3 x^{x} \left(\log{\left(x \right)} + \frac{x - 1}{x}\right) \left(x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) + x^{x} \left(x^{2 x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 x^{x} \left(\left(\log{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\log{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} + 1\right)}{x} + \frac{\log{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) + \left(\log{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + \frac{3 \left(\log{\left(x \right)} + 1\right)^{2}}{x} + \frac{3 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)}}{x} - \frac{3 \left(\log{\left(x \right)} + 1\right)}{x^{2}} - \frac{\log{\left(x \right)}}{x^{2}} + \frac{3}{x^{2}} + \frac{2}{x^{3}}\right) + \left(\log{\left(x \right)} + \frac{x - 1}{x}\right)^{3} + \frac{3 \left(2 - \frac{x - 1}{x}\right) \left(\log{\left(x \right)} + \frac{x - 1}{x}\right)}{x} - \frac{3 - \frac{2 \left(x - 1\right)}{x}}{x^{2}}\right)$$