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

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