There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{1}{sqrt(1 + 8{e}^{x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{sqrt(8{e}^{x} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{sqrt(8{e}^{x} + 1)}\right)}{dx}\\=&\frac{-(8({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)*\frac{1}{2}}{(8{e}^{x} + 1)(8{e}^{x} + 1)^{\frac{1}{2}}}\\=&\frac{-4{e}^{x}}{(8{e}^{x} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4{e}^{x}}{(8{e}^{x} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&-4(\frac{\frac{-3}{2}(8({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)}{(8{e}^{x} + 1)^{\frac{5}{2}}}){e}^{x} - \frac{4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))}{(8{e}^{x} + 1)^{\frac{3}{2}}}\\=&\frac{48{e}^{(2x)}}{(8{e}^{x} + 1)^{\frac{5}{2}}} - \frac{4{e}^{x}}{(8{e}^{x} + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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