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

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