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。\[ \begin{equation}\begin{split}【1/1】求函数{x}^{2}({e}^{(xx)} - 1) 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{2}{e}^{x^{2}} - x^{2}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( x^{2}{e}^{x^{2}} - x^{2}\right)}{dx}\\=&2x{e}^{x^{2}} + x^{2}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) - 2x\\=&2x{e}^{x^{2}} + 2x^{3}{e}^{x^{2}} - 2x\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 2x{e}^{x^{2}} + 2x^{3}{e}^{x^{2}} - 2x\right)}{dx}\\=&2{e}^{x^{2}} + 2x({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 2*3x^{2}{e}^{x^{2}} + 2x^{3}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) - 2\\=&2{e}^{x^{2}} + 10x^{2}{e}^{x^{2}} + 4x^{4}{e}^{x^{2}} - 2\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( 2{e}^{x^{2}} + 10x^{2}{e}^{x^{2}} + 4x^{4}{e}^{x^{2}} - 2\right)}{dx}\\=&2({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 10*2x{e}^{x^{2}} + 10x^{2}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 4*4x^{3}{e}^{x^{2}} + 4x^{4}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 0\\=&24x{e}^{x^{2}} + 36x^{3}{e}^{x^{2}} + 8x^{5}{e}^{x^{2}}\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( 24x{e}^{x^{2}} + 36x^{3}{e}^{x^{2}} + 8x^{5}{e}^{x^{2}}\right)}{dx}\\=&24{e}^{x^{2}} + 24x({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 36*3x^{2}{e}^{x^{2}} + 36x^{3}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)})) + 8*5x^{4}{e}^{x^{2}} + 8x^{5}({e}^{x^{2}}((2x)ln(e) + \frac{(x^{2})(0)}{(e)}))\\=&24{e}^{x^{2}} + 156x^{2}{e}^{x^{2}} + 112x^{4}{e}^{x^{2}} + 16x^{6}{e}^{x^{2}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!