There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {e}^{x} + ln(x){\frac{1}{x}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {\frac{1}{x}}^{x}ln(x) + {e}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {\frac{1}{x}}^{x}ln(x) + {e}^{x}\right)}{dx}\\=&({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(x) + \frac{{\frac{1}{x}}^{x}}{(x)} + ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(x) - {\frac{1}{x}}^{x}ln(x) + \frac{{\frac{1}{x}}^{x}}{x} + {e}^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {\frac{1}{x}}^{x}ln(\frac{1}{x})ln(x) - {\frac{1}{x}}^{x}ln(x) + \frac{{\frac{1}{x}}^{x}}{x} + {e}^{x}\right)}{dx}\\=&({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})ln(x) + \frac{{\frac{1}{x}}^{x}*-ln(x)}{(\frac{1}{x})x^{2}} + \frac{{\frac{1}{x}}^{x}ln(\frac{1}{x})}{(x)} - ({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(x) - \frac{{\frac{1}{x}}^{x}}{(x)} + \frac{-{\frac{1}{x}}^{x}}{x^{2}} + \frac{({\frac{1}{x}}^{x}((1)ln(\frac{1}{x}) + \frac{(x)(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{x} + ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&{\frac{1}{x}}^{x}ln^{2}(\frac{1}{x})ln(x) - 2{\frac{1}{x}}^{x}ln(\frac{1}{x})ln(x) - \frac{{\frac{1}{x}}^{x}ln(x)}{x} + \frac{2{\frac{1}{x}}^{x}ln(\frac{1}{x})}{x} + {\frac{1}{x}}^{x}ln(x) - \frac{2{\frac{1}{x}}^{x}}{x} - \frac{{\frac{1}{x}}^{x}}{x^{2}} + {e}^{x}\\ \end{split}\end{equation} \]

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