There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {2}^{x}lg(e^{-x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {2}^{x}lg(e^{-x})\right)}{dx}\\=&({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))lg(e^{-x}) + \frac{{2}^{x}e^{-x}*-1}{ln{10}(e^{-x})}\\=&{2}^{x}ln(2)lg(e^{-x}) - \frac{{2}^{x}}{ln{10}}\\ \end{split}\end{equation} \]

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