There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {e}^{(\frac{{x}^{2}}{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(\frac{1}{2}x^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&x{e}^{(\frac{1}{2}x^{2})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( x{e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&{e}^{(\frac{1}{2}x^{2})} + x({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&{e}^{(\frac{1}{2}x^{2})} + x^{2}{e}^{(\frac{1}{2}x^{2})}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {e}^{(\frac{1}{2}x^{2})} + x^{2}{e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)})) + 2x{e}^{(\frac{1}{2}x^{2})} + x^{2}({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&3x{e}^{(\frac{1}{2}x^{2})} + x^{3}{e}^{(\frac{1}{2}x^{2})}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3x{e}^{(\frac{1}{2}x^{2})} + x^{3}{e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&3{e}^{(\frac{1}{2}x^{2})} + 3x({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)})) + 3x^{2}{e}^{(\frac{1}{2}x^{2})} + x^{3}({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&3{e}^{(\frac{1}{2}x^{2})} + 6x^{2}{e}^{(\frac{1}{2}x^{2})} + x^{4}{e}^{(\frac{1}{2}x^{2})}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！