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

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