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

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