There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(p - c - t(p + c + f))}{(t(b - (p + c + f)))}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{pt}{(bt - pt - ct - ft)} - \frac{ct}{(bt - pt - ct - ft)} + \frac{p}{(bt - pt - ct - ft)} - \frac{c}{(bt - pt - ct - ft)} - \frac{ft}{(bt - pt - ct - ft)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{pt}{(bt - pt - ct - ft)} - \frac{ct}{(bt - pt - ct - ft)} + \frac{p}{(bt - pt - ct - ft)} - \frac{c}{(bt - pt - ct - ft)} - \frac{ft}{(bt - pt - ct - ft)}\right)}{dt}\\=& - (\frac{-(b - p - c - f)}{(bt - pt - ct - ft)^{2}})pt - \frac{p}{(bt - pt - ct - ft)} - (\frac{-(b - p - c - f)}{(bt - pt - ct - ft)^{2}})ct - \frac{c}{(bt - pt - ct - ft)} + (\frac{-(b - p - c - f)}{(bt - pt - ct - ft)^{2}})p + 0 - (\frac{-(b - p - c - f)}{(bt - pt - ct - ft)^{2}})c + 0 - (\frac{-(b - p - c - f)}{(bt - pt - ct - ft)^{2}})ft - \frac{f}{(bt - pt - ct - ft)}\\=&\frac{pbt}{(bt - pt - ct - ft)^{2}} - \frac{p^{2}t}{(bt - pt - ct - ft)^{2}} - \frac{2pct}{(bt - pt - ct - ft)^{2}} - \frac{2pft}{(bt - pt - ct - ft)^{2}} - \frac{pb}{(bt - pt - ct - ft)^{2}} + \frac{cbt}{(bt - pt - ct - ft)^{2}} - \frac{c^{2}t}{(bt - pt - ct - ft)^{2}} - \frac{2cft}{(bt - pt - ct - ft)^{2}} + \frac{cb}{(bt - pt - ct - ft)^{2}} + \frac{pf}{(bt - pt - ct - ft)^{2}} + \frac{p^{2}}{(bt - pt - ct - ft)^{2}} - \frac{cf}{(bt - pt - ct - ft)^{2}} - \frac{c^{2}}{(bt - pt - ct - ft)^{2}} + \frac{fbt}{(bt - pt - ct - ft)^{2}} - \frac{p}{(bt - pt - ct - ft)} - \frac{c}{(bt - pt - ct - ft)} - \frac{f^{2}t}{(bt - pt - ct - ft)^{2}} - \frac{f}{(bt - pt - ct - ft)}\\ \end{split}\end{equation} \]

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