There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arctan(\frac{(3x - 2)}{(3x + 2)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan(\frac{3x}{(3x + 2)} - \frac{2}{(3x + 2)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(\frac{3x}{(3x + 2)} - \frac{2}{(3x + 2)})\right)}{dx}\\=&(\frac{(3(\frac{-(3 + 0)}{(3x + 2)^{2}})x + \frac{3}{(3x + 2)} - 2(\frac{-(3 + 0)}{(3x + 2)^{2}}))}{(1 + (\frac{3x}{(3x + 2)} - \frac{2}{(3x + 2)})^{2})})\\=&\frac{-9x}{(3x + 2)^{2}(\frac{9x^{2}}{(3x + 2)^{2}} - \frac{12x}{(3x + 2)^{2}} + \frac{4}{(3x + 2)^{2}} + 1)} + \frac{6}{(3x + 2)^{2}(\frac{9x^{2}}{(3x + 2)^{2}} - \frac{12x}{(3x + 2)^{2}} + \frac{4}{(3x + 2)^{2}} + 1)} + \frac{3}{(3x + 2)(\frac{9x^{2}}{(3x + 2)^{2}} - \frac{12x}{(3x + 2)^{2}} + \frac{4}{(3x + 2)^{2}} + 1)}\\ \end{split}\end{equation} \]

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