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

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