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

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