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

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