There are 1 questions in this calculation: for each question, the 1 derivative of r is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (-PA{r}^{3} + (PA + C){r}^{3} - (C + 2mn{P}^{2}A)r){\frac{1}{(2rPA - C)}}^{2}\ with\ respect\ to\ r：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{Cr^{3}}{(2PAr - C)^{2}} - \frac{Cr}{(2PAr - C)^{2}} - \frac{2P^{2}Amnr}{(2PAr - C)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{Cr^{3}}{(2PAr - C)^{2}} - \frac{Cr}{(2PAr - C)^{2}} - \frac{2P^{2}Amnr}{(2PAr - C)^{2}}\right)}{dr}\\=&(\frac{-2(2PA + 0)}{(2PAr - C)^{3}})Cr^{3} + \frac{C*3r^{2}}{(2PAr - C)^{2}} - (\frac{-2(2PA + 0)}{(2PAr - C)^{3}})Cr - \frac{C}{(2PAr - C)^{2}} - 2(\frac{-2(2PA + 0)}{(2PAr - C)^{3}})P^{2}Amnr - \frac{2P^{2}Amn}{(2PAr - C)^{2}}\\=& - \frac{4PACr^{3}}{(2PAr - C)^{3}} + \frac{3Cr^{2}}{(2PAr - C)^{2}} + \frac{4PACr}{(2PAr - C)^{3}} - \frac{C}{(2PAr - C)^{2}} + \frac{8P^{3}A^{2}mnr}{(2PAr - C)^{3}} - \frac{2P^{2}Amn}{(2PAr - C)^{2}}\\ \end{split}\end{equation} \]

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