There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ a + bx - {e}^{x}((f)cos(2x) + (g)sin(2x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = a + bx - f{e}^{x}cos(2x) - g{e}^{x}sin(2x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( a + bx - f{e}^{x}cos(2x) - g{e}^{x}sin(2x)\right)}{dx}\\=&0 + b - f({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) - f{e}^{x}*-sin(2x)*2 - g({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) - g{e}^{x}cos(2x)*2\\=&b - f{e}^{x}cos(2x) + 2f{e}^{x}sin(2x) - g{e}^{x}sin(2x) - 2g{e}^{x}cos(2x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( b - f{e}^{x}cos(2x) + 2f{e}^{x}sin(2x) - g{e}^{x}sin(2x) - 2g{e}^{x}cos(2x)\right)}{dx}\\=&0 - f({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) - f{e}^{x}*-sin(2x)*2 + 2f({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) + 2f{e}^{x}cos(2x)*2 - g({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) - g{e}^{x}cos(2x)*2 - 2g({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) - 2g{e}^{x}*-sin(2x)*2\\=&3f{e}^{x}cos(2x) + 4f{e}^{x}sin(2x) + 3g{e}^{x}sin(2x) - 4g{e}^{x}cos(2x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 3f{e}^{x}cos(2x) + 4f{e}^{x}sin(2x) + 3g{e}^{x}sin(2x) - 4g{e}^{x}cos(2x)\right)}{dx}\\=&3f({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) + 3f{e}^{x}*-sin(2x)*2 + 4f({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) + 4f{e}^{x}cos(2x)*2 + 3g({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) + 3g{e}^{x}cos(2x)*2 - 4g({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) - 4g{e}^{x}*-sin(2x)*2\\=&11f{e}^{x}cos(2x) - 2f{e}^{x}sin(2x) + 11g{e}^{x}sin(2x) + 2g{e}^{x}cos(2x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 11f{e}^{x}cos(2x) - 2f{e}^{x}sin(2x) + 11g{e}^{x}sin(2x) + 2g{e}^{x}cos(2x)\right)}{dx}\\=&11f({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) + 11f{e}^{x}*-sin(2x)*2 - 2f({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) - 2f{e}^{x}cos(2x)*2 + 11g({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(2x) + 11g{e}^{x}cos(2x)*2 + 2g({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2x) + 2g{e}^{x}*-sin(2x)*2\\=&7f{e}^{x}cos(2x) - 24f{e}^{x}sin(2x) + 7g{e}^{x}sin(2x) + 24g{e}^{x}cos(2x)\\ \end{split}\end{equation} \]

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