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

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