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

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