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

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