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

Your problem has not been solved here? Please take a look at the  hot problems ！