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。\[ \begin{equation}\begin{split}【1/1】求函数log_{x}^{1} 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( log_{x}^{1}\right)}{dx}\\=&(\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))})\\=&\frac{-log_{x}^{1}}{xln(x)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{-log_{x}^{1}}{xln(x)}\right)}{dx}\\=&\frac{--log_{x}^{1}}{x^{2}ln(x)} - \frac{(\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))})}{xln(x)} - \frac{log_{x}^{1}*-1}{xln^{2}(x)(x)}\\=&\frac{log_{x}^{1}}{x^{2}ln(x)} + \frac{2log_{x}^{1}}{x^{2}ln^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( \frac{log_{x}^{1}}{x^{2}ln(x)} + \frac{2log_{x}^{1}}{x^{2}ln^{2}(x)}\right)}{dx}\\=&\frac{-2log_{x}^{1}}{x^{3}ln(x)} + \frac{(\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))})}{x^{2}ln(x)} + \frac{log_{x}^{1}*-1}{x^{2}ln^{2}(x)(x)} + \frac{2*-2log_{x}^{1}}{x^{3}ln^{2}(x)} + \frac{2(\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))})}{x^{2}ln^{2}(x)} + \frac{2log_{x}^{1}*-2}{x^{2}ln^{3}(x)(x)}\\=&\frac{-2log_{x}^{1}}{x^{3}ln(x)} - \frac{6log_{x}^{1}}{x^{3}ln^{2}(x)} - \frac{6log_{x}^{1}}{x^{3}ln^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( \frac{-2log_{x}^{1}}{x^{3}ln(x)} - \frac{6log_{x}^{1}}{x^{3}ln^{2}(x)} - \frac{6log_{x}^{1}}{x^{3}ln^{3}(x)}\right)}{dx}\\=&\frac{-2*-3log_{x}^{1}}{x^{4}ln(x)} - \frac{2(\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))})}{x^{3}ln(x)} - \frac{2log_{x}^{1}*-1}{x^{3}ln^{2}(x)(x)} - \frac{6*-3log_{x}^{1}}{x^{4}ln^{2}(x)} - \frac{6(\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))})}{x^{3}ln^{2}(x)} - \frac{6log_{x}^{1}*-2}{x^{3}ln^{3}(x)(x)} - \frac{6*-3log_{x}^{1}}{x^{4}ln^{3}(x)} - \frac{6(\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))})}{x^{3}ln^{3}(x)} - \frac{6log_{x}^{1}*-3}{x^{3}ln^{4}(x)(x)}\\=&\frac{6log_{x}^{1}}{x^{4}ln(x)} + \frac{22log_{x}^{1}}{x^{4}ln^{2}(x)} + \frac{36log_{x}^{1}}{x^{4}ln^{3}(x)} + \frac{24log_{x}^{1}}{x^{4}ln^{4}(x)}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!