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

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