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

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