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

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