There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(sqrt(1 + 2x) - 3)}{(sqrt(x) - 2)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{sqrt(2x + 1)}{(sqrt(x) - 2)} - \frac{3}{(sqrt(x) - 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{sqrt(2x + 1)}{(sqrt(x) - 2)} - \frac{3}{(sqrt(x) - 2)}\right)}{dx}\\=&(\frac{-(\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}} + 0)}{(sqrt(x) - 2)^{2}})sqrt(2x + 1) + \frac{(2 + 0)*\frac{1}{2}}{(sqrt(x) - 2)(2x + 1)^{\frac{1}{2}}} - 3(\frac{-(\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}} + 0)}{(sqrt(x) - 2)^{2}})\\=&\frac{-sqrt(2x + 1)}{2(sqrt(x) - 2)^{2}x^{\frac{1}{2}}} + \frac{1}{(sqrt(x) - 2)(2x + 1)^{\frac{1}{2}}} + \frac{3}{2(sqrt(x) - 2)^{2}x^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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