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

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