There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arctan(\frac{(2{x}^{\frac{1}{2}} - 1)}{sqrt(3)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(\frac{2{x}^{\frac{1}{2}}}{sqrt(3)} - \frac{1}{sqrt(3)})\right)}{dx}\\=&(\frac{(\frac{2({x}^{\frac{1}{2}}((0)ln(x) + \frac{(\frac{1}{2})(1)}{(x)}))}{sqrt(3)} + \frac{2{x}^{\frac{1}{2}}*-0*\frac{1}{2}*3^{\frac{1}{2}}}{(3)} - \frac{-0*\frac{1}{2}*3^{\frac{1}{2}}}{(3)})}{(1 + (\frac{2{x}^{\frac{1}{2}}}{sqrt(3)} - \frac{1}{sqrt(3)})^{2})})\\=&\frac{1}{(\frac{4x}{sqrt(3)^{2}} - \frac{4x^{\frac{1}{2}}}{sqrt(3)^{2}} + \frac{1}{sqrt(3)^{2}} + 1)x^{\frac{1}{2}}sqrt(3)}\\ \end{split}\end{equation} \]

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