本次共计算 1 个题目:每一题对 x 求 4 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数{e}^{(\frac{{x}^{2}}{2})} 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {e}^{(\frac{1}{2}x^{2})}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( {e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&x{e}^{(\frac{1}{2}x^{2})}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( x{e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&{e}^{(\frac{1}{2}x^{2})} + x({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&{e}^{(\frac{1}{2}x^{2})} + x^{2}{e}^{(\frac{1}{2}x^{2})}\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( {e}^{(\frac{1}{2}x^{2})} + x^{2}{e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)})) + 2x{e}^{(\frac{1}{2}x^{2})} + x^{2}({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&3x{e}^{(\frac{1}{2}x^{2})} + x^{3}{e}^{(\frac{1}{2}x^{2})}\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( 3x{e}^{(\frac{1}{2}x^{2})} + x^{3}{e}^{(\frac{1}{2}x^{2})}\right)}{dx}\\=&3{e}^{(\frac{1}{2}x^{2})} + 3x({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)})) + 3x^{2}{e}^{(\frac{1}{2}x^{2})} + x^{3}({e}^{(\frac{1}{2}x^{2})}((\frac{1}{2}*2x)ln(e) + \frac{(\frac{1}{2}x^{2})(0)}{(e)}))\\=&3{e}^{(\frac{1}{2}x^{2})} + 6x^{2}{e}^{(\frac{1}{2}x^{2})} + x^{4}{e}^{(\frac{1}{2}x^{2})}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!