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

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