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

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