There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {x}^{{x}^{{x}^{x}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{{x}^{{x}^{x}}}\right)}{dx}\\=&({x}^{{x}^{{x}^{x}}}((({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{x}})(1)}{(x)}))\\=&{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{3}(x) + {x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{2}(x) + \frac{{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln(x)}{x} + \frac{{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{3}(x) + {x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{2}(x) + \frac{{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln(x)}{x} + \frac{{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}}{x}\right)}{dx}\\=&({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})){x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{3}(x) + {x}^{x}({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})){x}^{{x}^{{x}^{x}}}ln^{3}(x) + {x}^{x}{x}^{{x}^{x}}({x}^{{x}^{{x}^{x}}}((({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{x}})(1)}{(x)}))ln^{3}(x) + \frac{{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}*3ln^{2}(x)}{(x)} + ({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})){x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{2}(x) + {x}^{x}({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})){x}^{{x}^{{x}^{x}}}ln^{2}(x) + {x}^{x}{x}^{{x}^{x}}({x}^{{x}^{{x}^{x}}}((({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{x}})(1)}{(x)}))ln^{2}(x) + \frac{{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}*2ln(x)}{(x)} + \frac{-{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln(x)}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})){x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln(x)}{x} + \frac{{x}^{x}({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})){x}^{{x}^{{x}^{x}}}ln(x)}{x} + \frac{{x}^{x}{x}^{{x}^{x}}({x}^{{x}^{{x}^{x}}}((({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{x}})(1)}{(x)}))ln(x)}{x} + \frac{{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}}{x(x)} + \frac{-{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}}{x^{2}} + \frac{({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})){x}^{{x}^{{x}^{x}}}}{x} + \frac{{x}^{{x}^{x}}({x}^{{x}^{{x}^{x}}}((({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{x}})(1)}{(x)}))}{x}\\=&{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{4}(x) + 2{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{3}(x) + {x}^{(2x)}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{5}(x) + 2{x}^{(2x)}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{4}(x) + \frac{2{x}^{(2x)}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{3}(x)}{x} + {x}^{(2x)}{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}ln^{6}(x) + 2{x}^{(2x)}{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}ln^{5}(x) + \frac{{x}^{(2x)}{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}ln^{4}(x)}{x} + \frac{{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}{x}^{x}ln^{3}(x)}{x} + \frac{3{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}{x}^{x}ln^{2}(x)}{x} + {x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{2}(x) + {x}^{(2x)}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{3}(x) + \frac{2{x}^{(2x)}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{2}(x)}{x} + {x}^{(2x)}{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}ln^{4}(x) + \frac{{x}^{(2x)}{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}ln^{3}(x)}{x} + \frac{{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}{x}^{x}ln^{2}(x)}{x} + \frac{2{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}{x}^{x}ln(x)}{x} - \frac{{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln(x)}{x^{2}} + \frac{2{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln^{2}(x)}{x} + \frac{2{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln(x)}{x} + \frac{{x}^{(2x)}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}ln(x)}{x^{2}} + \frac{{x}^{(2{x}^{x})}{x}^{(2x)}{x}^{{x}^{{x}^{x}}}ln^{4}(x)}{x} + \frac{{x}^{(2{x}^{x})}{x}^{(2x)}{x}^{{x}^{{x}^{x}}}ln^{3}(x)}{x} + \frac{{x}^{(2{x}^{x})}{x}^{(2x)}{x}^{{x}^{{x}^{x}}}ln^{2}(x)}{x^{2}} + \frac{{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}{x}^{x}ln(x)}{x^{2}} + \frac{{x}^{(2{x}^{x})}{x}^{x}{x}^{{x}^{{x}^{x}}}ln^{3}(x)}{x} + \frac{{x}^{(2{x}^{x})}{x}^{x}{x}^{{x}^{{x}^{x}}}ln^{2}(x)}{x} + \frac{{x}^{(2{x}^{x})}{x}^{x}{x}^{{x}^{{x}^{x}}}ln(x)}{x^{2}} + \frac{2{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}}{x^{2}} - \frac{{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}}{x^{2}} + \frac{{x}^{(2{x}^{x})}{x}^{{x}^{{x}^{x}}}}{x^{2}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！