There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ (\frac{({e}^{(\frac{x}{2})})x}{cos(2)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x{e}^{(\frac{1}{2}x)}}{cos(2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x{e}^{(\frac{1}{2}x)}}{cos(2)}\right)}{dx}\\=&\frac{{e}^{(\frac{1}{2}x)}}{cos(2)} + \frac{x({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))}{cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}sin(2)*0}{cos^{2}(2)}\\=&\frac{{e}^{(\frac{1}{2}x)}}{cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}}{2cos(2)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{e}^{(\frac{1}{2}x)}}{cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}}{2cos(2)}\right)}{dx}\\=&\frac{({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))}{cos(2)} + \frac{{e}^{(\frac{1}{2}x)}sin(2)*0}{cos^{2}(2)} + \frac{{e}^{(\frac{1}{2}x)}}{2cos(2)} + \frac{x({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))}{2cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}sin(2)*0}{2cos^{2}(2)}\\=&\frac{{e}^{(\frac{1}{2}x)}}{cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}}{4cos(2)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{{e}^{(\frac{1}{2}x)}}{cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}}{4cos(2)}\right)}{dx}\\=&\frac{({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))}{cos(2)} + \frac{{e}^{(\frac{1}{2}x)}sin(2)*0}{cos^{2}(2)} + \frac{{e}^{(\frac{1}{2}x)}}{4cos(2)} + \frac{x({e}^{(\frac{1}{2}x)}((\frac{1}{2})ln(e) + \frac{(\frac{1}{2}x)(0)}{(e)}))}{4cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}sin(2)*0}{4cos^{2}(2)}\\=&\frac{3{e}^{(\frac{1}{2}x)}}{4cos(2)} + \frac{x{e}^{(\frac{1}{2}x)}}{8cos(2)}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems ！
