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