There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{2} + 2x)}{(x + \frac{ln(x)}{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x + \frac{1}{2}ln(x))} + \frac{2x}{(x + \frac{1}{2}ln(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x + \frac{1}{2}ln(x))} + \frac{2x}{(x + \frac{1}{2}ln(x))}\right)}{dx}\\=&(\frac{-(1 + \frac{\frac{1}{2}}{(x)})}{(x + \frac{1}{2}ln(x))^{2}})x^{2} + \frac{2x}{(x + \frac{1}{2}ln(x))} + 2(\frac{-(1 + \frac{\frac{1}{2}}{(x)})}{(x + \frac{1}{2}ln(x))^{2}})x + \frac{2}{(x + \frac{1}{2}ln(x))}\\=& - \frac{5x}{2(x + \frac{1}{2}ln(x))^{2}} + \frac{2x}{(x + \frac{1}{2}ln(x))} - \frac{x^{2}}{(x + \frac{1}{2}ln(x))^{2}} - \frac{1}{(x + \frac{1}{2}ln(x))^{2}} + \frac{2}{(x + \frac{1}{2}ln(x))}\\ \end{split}\end{equation} \]

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