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

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