There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ log_{x}^{e{\frac{1}{x}}^{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = log_{x}^{\frac{e}{x^{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{x}^{\frac{e}{x^{2}}}\right)}{dx}\\=&(\frac{(\frac{(\frac{-2e}{x^{3}} + \frac{0}{x^{2}})}{(\frac{e}{x^{2}})} - \frac{(1)log_{x}^{\frac{e}{x^{2}}}}{(x)})}{(ln(x))})\\=&\frac{-2}{xln(x)} - \frac{log_{x}^{\frac{e}{x^{2}}}}{xln(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2}{xln(x)} - \frac{log_{x}^{\frac{e}{x^{2}}}}{xln(x)}\right)}{dx}\\=&\frac{-2*-1}{x^{2}ln(x)} - \frac{2*-1}{xln^{2}(x)(x)} - \frac{-log_{x}^{\frac{e}{x^{2}}}}{x^{2}ln(x)} - \frac{(\frac{(\frac{(\frac{-2e}{x^{3}} + \frac{0}{x^{2}})}{(\frac{e}{x^{2}})} - \frac{(1)log_{x}^{\frac{e}{x^{2}}}}{(x)})}{(ln(x))})}{xln(x)} - \frac{log_{x}^{\frac{e}{x^{2}}}*-1}{xln^{2}(x)(x)}\\=&\frac{2}{x^{2}ln(x)} + \frac{4}{x^{2}ln^{2}(x)} + \frac{log_{x}^{\frac{e}{x^{2}}}}{x^{2}ln(x)} + \frac{2log_{x}^{\frac{e}{x^{2}}}}{x^{2}ln^{2}(x)}\\ \end{split}\end{equation} \]

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