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

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