There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ e^{2x}(3cos(5x) - (2)sin(5x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3e^{2x}cos(5x) - 2e^{2x}sin(5x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3e^{2x}cos(5x) - 2e^{2x}sin(5x)\right)}{dx}\\=&3e^{2x}*2cos(5x) + 3e^{2x}*-sin(5x)*5 - 2e^{2x}*2sin(5x) - 2e^{2x}cos(5x)*5\\=&-4e^{2x}cos(5x) - 19e^{2x}sin(5x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -4e^{2x}cos(5x) - 19e^{2x}sin(5x)\right)}{dx}\\=&-4e^{2x}*2cos(5x) - 4e^{2x}*-sin(5x)*5 - 19e^{2x}*2sin(5x) - 19e^{2x}cos(5x)*5\\=&-103e^{2x}cos(5x) - 18e^{2x}sin(5x)\\ \end{split}\end{equation} \]

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