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

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