There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ x - (\frac{1}{3})(\frac{({x}^{3} - 3x - 1)}{({x}^{2} - 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x - \frac{\frac{1}{3}x^{3}}{(x^{2} - 1)} + \frac{x}{(x^{2} - 1)} + \frac{\frac{1}{3}}{(x^{2} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x - \frac{\frac{1}{3}x^{3}}{(x^{2} - 1)} + \frac{x}{(x^{2} - 1)} + \frac{\frac{1}{3}}{(x^{2} - 1)}\right)}{dx}\\=&1 - \frac{1}{3}(\frac{-(2x + 0)}{(x^{2} - 1)^{2}})x^{3} - \frac{\frac{1}{3}*3x^{2}}{(x^{2} - 1)} + (\frac{-(2x + 0)}{(x^{2} - 1)^{2}})x + \frac{1}{(x^{2} - 1)} + \frac{1}{3}(\frac{-(2x + 0)}{(x^{2} - 1)^{2}})\\=&\frac{2x^{4}}{3(x^{2} - 1)^{2}} - \frac{x^{2}}{(x^{2} - 1)} - \frac{2x^{2}}{(x^{2} - 1)^{2}} - \frac{2x}{3(x^{2} - 1)^{2}} + \frac{1}{(x^{2} - 1)} + 1\\ \end{split}\end{equation} \]

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