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

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