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

\[ \begin{equation}\begin{split}[2/2]Find\ the\ first\ derivative\ of\ function\ arctan(\frac{(1 + x)}{(1 - x)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan(\frac{x}{(-x + 1)} + \frac{1}{(-x + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(\frac{x}{(-x + 1)} + \frac{1}{(-x + 1)})\right)}{dx}\\=&(\frac{((\frac{-(-1 + 0)}{(-x + 1)^{2}})x + \frac{1}{(-x + 1)} + (\frac{-(-1 + 0)}{(-x + 1)^{2}}))}{(1 + (\frac{x}{(-x + 1)} + \frac{1}{(-x + 1)})^{2})})\\=&\frac{x}{(-x + 1)^{2}(\frac{x^{2}}{(-x + 1)^{2}} + \frac{2x}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)} + \frac{1}{(-x + 1)^{2}(\frac{x^{2}}{(-x + 1)^{2}} + \frac{2x}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)} + \frac{1}{(-x + 1)(\frac{x^{2}}{(-x + 1)^{2}} + \frac{2x}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + 1)}\\ \end{split}\end{equation} \]

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