There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ ({e}^{(3x)})sin(3x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(3x)}sin(3x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(3x)}sin(3x)\right)}{dx}\\=&({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)}))sin(3x) + {e}^{(3x)}cos(3x)*3\\=&3{e}^{(3x)}sin(3x) + 3{e}^{(3x)}cos(3x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3{e}^{(3x)}sin(3x) + 3{e}^{(3x)}cos(3x)\right)}{dx}\\=&3({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)}))sin(3x) + 3{e}^{(3x)}cos(3x)*3 + 3({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)}))cos(3x) + 3{e}^{(3x)}*-sin(3x)*3\\=&18{e}^{(3x)}cos(3x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 18{e}^{(3x)}cos(3x)\right)}{dx}\\=&18({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)}))cos(3x) + 18{e}^{(3x)}*-sin(3x)*3\\=&54{e}^{(3x)}cos(3x) - 54{e}^{(3x)}sin(3x)\\ \end{split}\end{equation} \]

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