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

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