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

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