There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2{e}^{t})}{(3 - {e}^{t})}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2{e}^{t}}{(-{e}^{t} + 3)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2{e}^{t}}{(-{e}^{t} + 3)}\right)}{dt}\\=&2(\frac{-(-({e}^{t}((1)ln(e) + \frac{(t)(0)}{(e)})) + 0)}{(-{e}^{t} + 3)^{2}}){e}^{t} + \frac{2({e}^{t}((1)ln(e) + \frac{(t)(0)}{(e)}))}{(-{e}^{t} + 3)}\\=&\frac{2{e}^{(2t)}}{(-{e}^{t} + 3)^{2}} + \frac{2{e}^{t}}{(-{e}^{t} + 3)}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！