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

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