There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(x) - (x + 5)(\frac{(x - 1)}{(4x + 2)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x) - \frac{x^{2}}{(4x + 2)} - \frac{4x}{(4x + 2)} + \frac{5}{(4x + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(x) - \frac{x^{2}}{(4x + 2)} - \frac{4x}{(4x + 2)} + \frac{5}{(4x + 2)}\right)}{dx}\\=&\frac{1}{(x)} - (\frac{-(4 + 0)}{(4x + 2)^{2}})x^{2} - \frac{2x}{(4x + 2)} - 4(\frac{-(4 + 0)}{(4x + 2)^{2}})x - \frac{4}{(4x + 2)} + 5(\frac{-(4 + 0)}{(4x + 2)^{2}})\\=&\frac{1}{x} + \frac{4x^{2}}{(4x + 2)^{2}} - \frac{2x}{(4x + 2)} + \frac{16x}{(4x + 2)^{2}} - \frac{20}{(4x + 2)^{2}} - \frac{4}{(4x + 2)}\\ \end{split}\end{equation} \]

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