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

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