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

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