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

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