There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(p - c - D(t)(p + c + f))}{(D(t)(b - (p + c + f)))}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{pDt}{(Dbt - pDt - cDt - Dft)} - \frac{cDt}{(Dbt - pDt - cDt - Dft)} + \frac{p}{(Dbt - pDt - cDt - Dft)} - \frac{c}{(Dbt - pDt - cDt - Dft)} - \frac{Dft}{(Dbt - pDt - cDt - Dft)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{pDt}{(Dbt - pDt - cDt - Dft)} - \frac{cDt}{(Dbt - pDt - cDt - Dft)} + \frac{p}{(Dbt - pDt - cDt - Dft)} - \frac{c}{(Dbt - pDt - cDt - Dft)} - \frac{Dft}{(Dbt - pDt - cDt - Dft)}\right)}{dt}\\=& - (\frac{-(Db - pD - cD - Df)}{(Dbt - pDt - cDt - Dft)^{2}})pDt - \frac{pD}{(Dbt - pDt - cDt - Dft)} - (\frac{-(Db - pD - cD - Df)}{(Dbt - pDt - cDt - Dft)^{2}})cDt - \frac{cD}{(Dbt - pDt - cDt - Dft)} + (\frac{-(Db - pD - cD - Df)}{(Dbt - pDt - cDt - Dft)^{2}})p + 0 - (\frac{-(Db - pD - cD - Df)}{(Dbt - pDt - cDt - Dft)^{2}})c + 0 - (\frac{-(Db - pD - cD - Df)}{(Dbt - pDt - cDt - Dft)^{2}})Dft - \frac{Df}{(Dbt - pDt - cDt - Dft)}\\=&\frac{pD^{2}bt}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{p^{2}D^{2}t}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{2pcD^{2}t}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{2pD^{2}ft}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{pDb}{(Dbt - pDt - cDt - Dft)^{2}} + \frac{cD^{2}bt}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{c^{2}D^{2}t}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{2cD^{2}ft}{(Dbt - pDt - cDt - Dft)^{2}} + \frac{cDb}{(Dbt - pDt - cDt - Dft)^{2}} + \frac{pDf}{(Dbt - pDt - cDt - Dft)^{2}} + \frac{p^{2}D}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{pD}{(Dbt - pDt - cDt - Dft)} - \frac{cDf}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{c^{2}D}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{cD}{(Dbt - pDt - cDt - Dft)} + \frac{D^{2}fbt}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{D^{2}f^{2}t}{(Dbt - pDt - cDt - Dft)^{2}} - \frac{Df}{(Dbt - pDt - cDt - Dft)}\\ \end{split}\end{equation} \]

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