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

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