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

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