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

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