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

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