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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(sqrt({(\frac{(sqrt(x) + 1)}{2})}^{2} + \frac{9}{16}) - \frac{(sqrt(x) + 1)}{2})(sqrt(x) + 1)}{2} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{2}sqrt(x)sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16}) - \frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16}) - \frac{1}{2}sqrt(x) - \frac{1}{4}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{1}{2}sqrt(x)sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16}) - \frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16}) - \frac{1}{2}sqrt(x) - \frac{1}{4}\right)}{dx}\\=&\frac{\frac{1}{2}*\frac{1}{2}sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})}{(x)^{\frac{1}{2}}} + \frac{\frac{1}{2}sqrt(x)(\frac{\frac{1}{4}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + \frac{\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 0)*\frac{1}{2}}{(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} - \frac{\frac{1}{4}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + \frac{\frac{1}{2}(\frac{\frac{1}{4}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + \frac{\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 0)*\frac{1}{2}}{(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} - \frac{\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 0\\=&\frac{sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})}{4x^{\frac{1}{2}}} + \frac{sqrt(x)}{16(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} + \frac{sqrt(x)}{16(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}} + \frac{1}{16(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}} + \frac{1}{16(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} - \frac{1}{4x^{\frac{1}{2}}} - \frac{1}{4}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!