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

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