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

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