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

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