There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2 + 2x + 2ln(x))}{(({x}^{2}) + 2x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2x}{(x^{2} + 2x)} + \frac{2ln(x)}{(x^{2} + 2x)} + \frac{2}{(x^{2} + 2x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2x}{(x^{2} + 2x)} + \frac{2ln(x)}{(x^{2} + 2x)} + \frac{2}{(x^{2} + 2x)}\right)}{dx}\\=&2(\frac{-(2x + 2)}{(x^{2} + 2x)^{2}})x + \frac{2}{(x^{2} + 2x)} + 2(\frac{-(2x + 2)}{(x^{2} + 2x)^{2}})ln(x) + \frac{2}{(x^{2} + 2x)(x)} + 2(\frac{-(2x + 2)}{(x^{2} + 2x)^{2}})\\=& - \frac{4xln(x)}{(x^{2} + 2x)^{2}} - \frac{4x^{2}}{(x^{2} + 2x)^{2}} + \frac{2}{(x^{2} + 2x)x} - \frac{8x}{(x^{2} + 2x)^{2}} - \frac{4ln(x)}{(x^{2} + 2x)^{2}} + \frac{2}{(x^{2} + 2x)} - \frac{4}{(x^{2} + 2x)^{2}}\\ \end{split}\end{equation} \]

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