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

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