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

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