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

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