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

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