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

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