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。\[ \begin{equation}\begin{split}【1/1】求函数(x - 1){(x - 2)}^{2}{(x - 3)}^{3}{(x - 4)}^{3} 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{9} - 26x^{8} + 296x^{7} - 1934x^{6} + 7979x^{5} - 21512x^{4} + 37804x^{3} - 41616x^{2} + 25920x - 6912\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( x^{9} - 26x^{8} + 296x^{7} - 1934x^{6} + 7979x^{5} - 21512x^{4} + 37804x^{3} - 41616x^{2} + 25920x - 6912\right)}{dx}\\=&9x^{8} - 26*8x^{7} + 296*7x^{6} - 1934*6x^{5} + 7979*5x^{4} - 21512*4x^{3} + 37804*3x^{2} - 41616*2x + 25920 + 0\\=&9x^{8} - 208x^{7} + 2072x^{6} - 11604x^{5} + 39895x^{4} - 86048x^{3} + 113412x^{2} - 83232x + 25920\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 9x^{8} - 208x^{7} + 2072x^{6} - 11604x^{5} + 39895x^{4} - 86048x^{3} + 113412x^{2} - 83232x + 25920\right)}{dx}\\=&9*8x^{7} - 208*7x^{6} + 2072*6x^{5} - 11604*5x^{4} + 39895*4x^{3} - 86048*3x^{2} + 113412*2x - 83232 + 0\\=&72x^{7} - 1456x^{6} + 12432x^{5} - 58020x^{4} + 159580x^{3} - 258144x^{2} + 226824x - 83232\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( 72x^{7} - 1456x^{6} + 12432x^{5} - 58020x^{4} + 159580x^{3} - 258144x^{2} + 226824x - 83232\right)}{dx}\\=&72*7x^{6} - 1456*6x^{5} + 12432*5x^{4} - 58020*4x^{3} + 159580*3x^{2} - 258144*2x + 226824 + 0\\=&504x^{6} - 8736x^{5} + 62160x^{4} - 232080x^{3} + 478740x^{2} - 516288x + 226824\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( 504x^{6} - 8736x^{5} + 62160x^{4} - 232080x^{3} + 478740x^{2} - 516288x + 226824\right)}{dx}\\=&504*6x^{5} - 8736*5x^{4} + 62160*4x^{3} - 232080*3x^{2} + 478740*2x - 516288 + 0\\=&3024x^{5} - 43680x^{4} + 248640x^{3} - 696240x^{2} + 957480x - 516288\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!