There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(100 + 2*100 - 2x)(100 + x)}{(10000 + 100*100 - 100x)} - 1\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{100x}{(-100x + 20000)} - \frac{2x^{2}}{(-100x + 20000)} + \frac{30000}{(-100x + 20000)} - 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{100x}{(-100x + 20000)} - \frac{2x^{2}}{(-100x + 20000)} + \frac{30000}{(-100x + 20000)} - 1\right)}{dx}\\=&100(\frac{-(-100 + 0)}{(-100x + 20000)^{2}})x + \frac{100}{(-100x + 20000)} - 2(\frac{-(-100 + 0)}{(-100x + 20000)^{2}})x^{2} - \frac{2*2x}{(-100x + 20000)} + 30000(\frac{-(-100 + 0)}{(-100x + 20000)^{2}}) + 0\\=&\frac{10000x}{(-100x + 20000)^{2}} - \frac{200x^{2}}{(-100x + 20000)^{2}} - \frac{4x}{(-100x + 20000)} + \frac{3000000}{(-100x + 20000)^{2}} + \frac{100}{(-100x + 20000)}\\ \end{split}\end{equation} \]

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