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

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