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

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