There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(3x){e}^{(2x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(2x)}sin(3x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(2x)}sin(3x)\right)}{dx}\\=&({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x) + {e}^{(2x)}cos(3x)*3\\=&2{e}^{(2x)}sin(3x) + 3{e}^{(2x)}cos(3x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2{e}^{(2x)}sin(3x) + 3{e}^{(2x)}cos(3x)\right)}{dx}\\=&2({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x) + 2{e}^{(2x)}cos(3x)*3 + 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x) + 3{e}^{(2x)}*-sin(3x)*3\\=&-5{e}^{(2x)}sin(3x) + 12{e}^{(2x)}cos(3x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -5{e}^{(2x)}sin(3x) + 12{e}^{(2x)}cos(3x)\right)}{dx}\\=&-5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x) - 5{e}^{(2x)}cos(3x)*3 + 12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x) + 12{e}^{(2x)}*-sin(3x)*3\\=&-46{e}^{(2x)}sin(3x) + 9{e}^{(2x)}cos(3x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -46{e}^{(2x)}sin(3x) + 9{e}^{(2x)}cos(3x)\right)}{dx}\\=&-46({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x) - 46{e}^{(2x)}cos(3x)*3 + 9({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x) + 9{e}^{(2x)}*-sin(3x)*3\\=&-119{e}^{(2x)}sin(3x) - 120{e}^{(2x)}cos(3x)\\ \end{split}\end{equation} \]

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