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

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