There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ \frac{{e}^{x}{cos(2x)}^{1}}{2*2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{4}{e}^{x}cos(2x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{4}{e}^{x}cos(2x)\right)}{dx}\\=&\frac{1}{4}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) + \frac{1}{4}{e}^{x}*-sin(2x)*2\\=&\frac{{e}^{x}cos(2x)}{4} - \frac{{e}^{x}sin(2x)}{2}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{e}^{x}cos(2x)}{4} - \frac{{e}^{x}sin(2x)}{2}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x)}{4} + \frac{{e}^{x}*-sin(2x)*2}{4} - \frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x)}{2} - \frac{{e}^{x}cos(2x)*2}{2}\\=&\frac{-3{e}^{x}cos(2x)}{4} - {e}^{x}sin(2x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3{e}^{x}cos(2x)}{4} - {e}^{x}sin(2x)\right)}{dx}\\=&\frac{-3({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x)}{4} - \frac{3{e}^{x}*-sin(2x)*2}{4} - ({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) - {e}^{x}cos(2x)*2\\=&\frac{-11{e}^{x}cos(2x)}{4} + \frac{{e}^{x}sin(2x)}{2}\\ \end{split}\end{equation} \]

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