There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{x}{(2sqrt({x}^{2} + 4))} - \frac{(2 - x)}{(sqrt({(2 - x)}^{2}) + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{2}x}{sqrt(x^{2} + 4)} + \frac{x}{(sqrt(x^{2} - 4x + 4) + 1)} - \frac{2}{(sqrt(x^{2} - 4x + 4) + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{2}x}{sqrt(x^{2} + 4)} + \frac{x}{(sqrt(x^{2} - 4x + 4) + 1)} - \frac{2}{(sqrt(x^{2} - 4x + 4) + 1)}\right)}{dx}\\=&\frac{\frac{1}{2}}{sqrt(x^{2} + 4)} + \frac{\frac{1}{2}x*-(2x + 0)*\frac{1}{2}}{(x^{2} + 4)(x^{2} + 4)^{\frac{1}{2}}} + (\frac{-(\frac{(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}} + 0)}{(sqrt(x^{2} - 4x + 4) + 1)^{2}})x + \frac{1}{(sqrt(x^{2} - 4x + 4) + 1)} - 2(\frac{-(\frac{(2x - 4 + 0)*\frac{1}{2}}{(x^{2} - 4x + 4)^{\frac{1}{2}}} + 0)}{(sqrt(x^{2} - 4x + 4) + 1)^{2}})\\=&\frac{1}{2sqrt(x^{2} + 4)} - \frac{x^{2}}{2(x^{2} + 4)^{\frac{3}{2}}} - \frac{x^{2}}{(sqrt(x^{2} - 4x + 4) + 1)^{2}(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{4x}{(sqrt(x^{2} - 4x + 4) + 1)^{2}(x^{2} - 4x + 4)^{\frac{1}{2}}} - \frac{4}{(sqrt(x^{2} - 4x + 4) + 1)^{2}(x^{2} - 4x + 4)^{\frac{1}{2}}} + \frac{1}{(sqrt(x^{2} - 4x + 4) + 1)}\\ \end{split}\end{equation} \]

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