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

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