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

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