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。\[ \begin{equation}\begin{split}【1/1】求函数{2}^{\frac{1}{x}} 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( {2}^{\frac{1}{x}}\right)}{dx}\\=&({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))\\=&\frac{-{2}^{\frac{1}{x}}ln(2)}{x^{2}}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{-{2}^{\frac{1}{x}}ln(2)}{x^{2}}\right)}{dx}\\=&\frac{--2 * {2}^{\frac{1}{x}}ln(2)}{x^{3}} - \frac{({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln(2)}{x^{2}} - \frac{{2}^{\frac{1}{x}}*0}{x^{2}(2)}\\=&\frac{2 * {2}^{\frac{1}{x}}ln(2)}{x^{3}} + \frac{{2}^{\frac{1}{x}}ln^{2}(2)}{x^{4}}\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( \frac{2 * {2}^{\frac{1}{x}}ln(2)}{x^{3}} + \frac{{2}^{\frac{1}{x}}ln^{2}(2)}{x^{4}}\right)}{dx}\\=&\frac{2*-3 * {2}^{\frac{1}{x}}ln(2)}{x^{4}} + \frac{2({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln(2)}{x^{3}} + \frac{2 * {2}^{\frac{1}{x}}*0}{x^{3}(2)} + \frac{-4 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{5}} + \frac{({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln^{2}(2)}{x^{4}} + \frac{{2}^{\frac{1}{x}}*2ln(2)*0}{x^{4}(2)}\\=&\frac{-6 * {2}^{\frac{1}{x}}ln(2)}{x^{4}} - \frac{6 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{5}} - \frac{{2}^{\frac{1}{x}}ln^{3}(2)}{x^{6}}\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( \frac{-6 * {2}^{\frac{1}{x}}ln(2)}{x^{4}} - \frac{6 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{5}} - \frac{{2}^{\frac{1}{x}}ln^{3}(2)}{x^{6}}\right)}{dx}\\=&\frac{-6*-4 * {2}^{\frac{1}{x}}ln(2)}{x^{5}} - \frac{6({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln(2)}{x^{4}} - \frac{6 * {2}^{\frac{1}{x}}*0}{x^{4}(2)} - \frac{6*-5 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{6}} - \frac{6({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln^{2}(2)}{x^{5}} - \frac{6 * {2}^{\frac{1}{x}}*2ln(2)*0}{x^{5}(2)} - \frac{-6 * {2}^{\frac{1}{x}}ln^{3}(2)}{x^{7}} - \frac{({2}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(2) + \frac{(\frac{1}{x})(0)}{(2)}))ln^{3}(2)}{x^{6}} - \frac{{2}^{\frac{1}{x}}*3ln^{2}(2)*0}{x^{6}(2)}\\=&\frac{24 * {2}^{\frac{1}{x}}ln(2)}{x^{5}} + \frac{36 * {2}^{\frac{1}{x}}ln^{2}(2)}{x^{6}} + \frac{12 * {2}^{\frac{1}{x}}ln^{3}(2)}{x^{7}} + \frac{{2}^{\frac{1}{x}}ln^{4}(2)}{x^{8}}\\ \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!