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

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