本次共计算 1 个题目:每一题对 x 求 1 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数\frac{{(x + 2)}^{3}}{sqrt({(x + 1)}^{5}(x + 3))} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{3}}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{6x^{2}}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{12x}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{8}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{x^{3}}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{6x^{2}}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{12x}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{8}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)}\right)}{dx}\\=&\frac{3x^{2}}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{x^{3}*-(6x^{5} + 8*5x^{4} + 25*4x^{3} + 40*3x^{2} + 35*2x + 16 + 0)*\frac{1}{2}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{1}{2}}} + \frac{6*2x}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{6x^{2}*-(6x^{5} + 8*5x^{4} + 25*4x^{3} + 40*3x^{2} + 35*2x + 16 + 0)*\frac{1}{2}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{1}{2}}} + \frac{12}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} + \frac{12x*-(6x^{5} + 8*5x^{4} + 25*4x^{3} + 40*3x^{2} + 35*2x + 16 + 0)*\frac{1}{2}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{1}{2}}} + \frac{8*-(6x^{5} + 8*5x^{4} + 25*4x^{3} + 40*3x^{2} + 35*2x + 16 + 0)*\frac{1}{2}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{1}{2}}}\\=&\frac{3x^{2}}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} - \frac{3x^{8}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} - \frac{38x^{7}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} - \frac{206x^{6}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} - \frac{624x^{5}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} - \frac{1155x^{4}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} - \frac{1338x^{3}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} + \frac{12x}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} - \frac{948x^{2}}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} + \frac{12}{sqrt(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)} - \frac{376x}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{2}}} - \frac{64}{(x^{6} + 8x^{5} + 25x^{4} + 40x^{3} + 35x^{2} + 16x + 3)^{\frac{3}{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!