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

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