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

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