There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(\frac{(x - ({x}^{2} - 8))}{(x + ({x}^{2} - 8))})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})\right)}{dx}\\=&\frac{((\frac{-(1 + 2x + 0)}{(x + x^{2} - 8)^{2}})x + \frac{1}{(x + x^{2} - 8)} - (\frac{-(1 + 2x + 0)}{(x + x^{2} - 8)^{2}})x^{2} - \frac{2x}{(x + x^{2} - 8)} + 8(\frac{-(1 + 2x + 0)}{(x + x^{2} - 8)^{2}}))}{(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})}\\=&\frac{-x^{2}}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} + \frac{2x^{3}}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} - \frac{2x}{(x + x^{2} - 8)(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} - \frac{17x}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})} + \frac{1}{(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})(x + x^{2} - 8)} - \frac{8}{(x + x^{2} - 8)^{2}(\frac{x}{(x + x^{2} - 8)} - \frac{x^{2}}{(x + x^{2} - 8)} + \frac{8}{(x + x^{2} - 8)})}\\ \end{split}\end{equation} \]

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