There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 2x - ln(x) + \frac{(x - 1)}{(4(lg(x) - 1) + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2x - ln(x) + \frac{x}{(4lg(x) - 3)} - \frac{1}{(4lg(x) - 3)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x - ln(x) + \frac{x}{(4lg(x) - 3)} - \frac{1}{(4lg(x) - 3)}\right)}{dx}\\=&2 - \frac{1}{(x)} + (\frac{-(\frac{4}{ln{10}(x)} + 0)}{(4lg(x) - 3)^{2}})x + \frac{1}{(4lg(x) - 3)} - (\frac{-(\frac{4}{ln{10}(x)} + 0)}{(4lg(x) - 3)^{2}})\\=& - \frac{1}{x} - \frac{4}{(4lg(x) - 3)^{2}ln{10}} + \frac{4}{(4lg(x) - 3)^{2}xln{10}} + \frac{1}{(4lg(x) - 3)} + 2\\ \end{split}\end{equation} \]

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