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

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