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