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

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