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

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