There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{((x - 1){e}^{arctan(x)})}{(x{(1 + {x}^{2})}^{\frac{1}{2}})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{1}{2}}} - \frac{{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{1}{2}}x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{1}{2}}} - \frac{{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{1}{2}}x}\right)}{dx}\\=&(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{3}{2}}}){e}^{arctan(x)} + \frac{({e}^{arctan(x)}(((\frac{(1)}{(1 + (x)^{2})}))ln(e) + \frac{(arctan(x))(0)}{(e)}))}{(x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + 0)}{(x^{2} + 1)^{\frac{3}{2}}}){e}^{arctan(x)}}{x} - \frac{-{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{1}{2}}x^{2}} - \frac{({e}^{arctan(x)}(((\frac{(1)}{(1 + (x)^{2})}))ln(e) + \frac{(arctan(x))(0)}{(e)}))}{(x^{2} + 1)^{\frac{1}{2}}x}\\=&\frac{-x{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{3}{2}}} + \frac{2{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{3}{2}}} + \frac{{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{1}{2}}x^{2}} - \frac{{e}^{arctan(x)}}{(x^{2} + 1)^{\frac{3}{2}}x}\\ \end{split}\end{equation} \]

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