本次共计算 1 个题目:每一题对 x 求 2 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(x + 1)}{(1 - {\frac{1}{2}}^{x})} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x}{(-{\frac{1}{2}}^{x} + 1)} + \frac{1}{(-{\frac{1}{2}}^{x} + 1)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{x}{(-{\frac{1}{2}}^{x} + 1)} + \frac{1}{(-{\frac{1}{2}}^{x} + 1)}\right)}{dx}\\=&(\frac{-(-({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})})) + 0)}{(-{\frac{1}{2}}^{x} + 1)^{2}})x + \frac{1}{(-{\frac{1}{2}}^{x} + 1)} + (\frac{-(-({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})})) + 0)}{(-{\frac{1}{2}}^{x} + 1)^{2}})\\=&\frac{x{\frac{1}{2}}^{x}ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{{\frac{1}{2}}^{x}ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{1}{(-{\frac{1}{2}}^{x} + 1)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{x{\frac{1}{2}}^{x}ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{{\frac{1}{2}}^{x}ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{1}{(-{\frac{1}{2}}^{x} + 1)}\right)}{dx}\\=&(\frac{-2(-({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})})) + 0)}{(-{\frac{1}{2}}^{x} + 1)^{3}})x{\frac{1}{2}}^{x}ln(\frac{1}{2}) + \frac{{\frac{1}{2}}^{x}ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{x({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{x{\frac{1}{2}}^{x}*0}{(-{\frac{1}{2}}^{x} + 1)^{2}(\frac{1}{2})} + (\frac{-2(-({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})})) + 0)}{(-{\frac{1}{2}}^{x} + 1)^{3}}){\frac{1}{2}}^{x}ln(\frac{1}{2}) + \frac{({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{{\frac{1}{2}}^{x}*0}{(-{\frac{1}{2}}^{x} + 1)^{2}(\frac{1}{2})} + (\frac{-(-({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})})) + 0)}{(-{\frac{1}{2}}^{x} + 1)^{2}})\\=&\frac{2x{\frac{1}{2}}^{(2x)}ln^{2}(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{3}} + \frac{2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{x{\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{2}} + \frac{2 * {\frac{1}{2}}^{(2x)}ln^{2}(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{3}} + \frac{{\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})}{(-{\frac{1}{2}}^{x} + 1)^{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!