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

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