There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(arctan(x)x - \frac{ln(1 + {x}^{2})}{2} - \frac{π}{4})}{arctan(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x - \frac{\frac{1}{2}ln(x^{2} + 1)}{arctan(x)} - \frac{\frac{1}{4}π}{arctan(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x - \frac{\frac{1}{2}ln(x^{2} + 1)}{arctan(x)} - \frac{\frac{1}{4}π}{arctan(x)}\right)}{dx}\\=&1 - \frac{\frac{1}{2}(2x + 0)}{(x^{2} + 1)arctan(x)} - \frac{1}{2}ln(x^{2} + 1)(\frac{-(1)}{arctan^{2}(x)(1 + (x)^{2})}) - \frac{1}{4}π(\frac{-(1)}{arctan^{2}(x)(1 + (x)^{2})})\\=& - \frac{x}{(x^{2} + 1)arctan(x)} + \frac{ln(x^{2} + 1)}{2(x^{2} + 1)arctan^{2}(x)} + \frac{π}{4(x^{2} + 1)arctan^{2}(x)} + 1\\ \end{split}\end{equation} \]

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