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

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