There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(25 - 20x)}{({(100x - x(1 - x))}^{\frac{1}{2}})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{20x}{(x^{2} + 99x)^{\frac{1}{2}}} + \frac{25}{(x^{2} + 99x)^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{20x}{(x^{2} + 99x)^{\frac{1}{2}}} + \frac{25}{(x^{2} + 99x)^{\frac{1}{2}}}\right)}{dx}\\=& - 20(\frac{\frac{-1}{2}(2x + 99)}{(x^{2} + 99x)^{\frac{3}{2}}})x - \frac{20}{(x^{2} + 99x)^{\frac{1}{2}}} + 25(\frac{\frac{-1}{2}(2x + 99)}{(x^{2} + 99x)^{\frac{3}{2}}})\\=&\frac{20x^{2}}{(x^{2} + 99x)^{\frac{3}{2}}} + \frac{965x}{(x^{2} + 99x)^{\frac{3}{2}}} - \frac{20}{(x^{2} + 99x)^{\frac{1}{2}}} - \frac{2475}{2(x^{2} + 99x)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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