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

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