There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1 + {2}^{x})}{(2x(1 - {x}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{2}^{x}}{(2x - 2x^{3})} + \frac{1}{(2x - 2x^{3})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{2}^{x}}{(2x - 2x^{3})} + \frac{1}{(2x - 2x^{3})}\right)}{dx}\\=&(\frac{-(2 - 2*3x^{2})}{(2x - 2x^{3})^{2}}){2}^{x} + \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{(2x - 2x^{3})} + (\frac{-(2 - 2*3x^{2})}{(2x - 2x^{3})^{2}})\\=&\frac{6x^{2}{2}^{x}}{(2x - 2x^{3})^{2}} + \frac{{2}^{x}ln(2)}{(2x - 2x^{3})} - \frac{2 * {2}^{x}}{(2x - 2x^{3})^{2}} + \frac{6x^{2}}{(2x - 2x^{3})^{2}} - \frac{2}{(2x - 2x^{3})^{2}}\\ \end{split}\end{equation} \]

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