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

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