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

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