There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{{e}^{3}x}{16} - (\frac{x}{4} + \frac{1}{16}){\frac{1}{e}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{16}xe^{3} - \frac{1}{4}x{\frac{1}{e}}^{x} - \frac{1}{16}{\frac{1}{e}}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{16}xe^{3} - \frac{1}{4}x{\frac{1}{e}}^{x} - \frac{1}{16}{\frac{1}{e}}^{x}\right)}{dx}\\=&\frac{1}{16}e^{3} + \frac{1}{16}x*3e^{2}*0 - \frac{1}{4}{\frac{1}{e}}^{x} - \frac{1}{4}x({\frac{1}{e}}^{x}((1)ln(\frac{1}{e}) + \frac{(x)(\frac{-0}{e^{2}})}{(\frac{1}{e})})) - \frac{1}{16}({\frac{1}{e}}^{x}((1)ln(\frac{1}{e}) + \frac{(x)(\frac{-0}{e^{2}})}{(\frac{1}{e})}))\\=&\frac{e^{3}}{16} - \frac{3{\frac{1}{e}}^{x}}{16} + \frac{x{\frac{1}{e}}^{x}}{4}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{e^{3}}{16} - \frac{3{\frac{1}{e}}^{x}}{16} + \frac{x{\frac{1}{e}}^{x}}{4}\right)}{dx}\\=&\frac{3e^{2}*0}{16} - \frac{3({\frac{1}{e}}^{x}((1)ln(\frac{1}{e}) + \frac{(x)(\frac{-0}{e^{2}})}{(\frac{1}{e})}))}{16} + \frac{{\frac{1}{e}}^{x}}{4} + \frac{x({\frac{1}{e}}^{x}((1)ln(\frac{1}{e}) + \frac{(x)(\frac{-0}{e^{2}})}{(\frac{1}{e})}))}{4}\\=&\frac{7{\frac{1}{e}}^{x}}{16} - \frac{x{\frac{1}{e}}^{x}}{4}\\ \end{split}\end{equation} \]

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