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

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