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

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