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

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