求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
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。
\[ \begin{equation}\begin{split}【1/1】求函数(sqrt({(\frac{(sqrt(x) + 1)}{2})}^{2} + \frac{9}{16}) - \frac{(sqrt(x) + 1)}{2})(sqrt(x) + 1) 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})sqrt(x) - \frac{1}{2}sqrt(x)^{2} + sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16}) - sqrt(x) - \frac{1}{2}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})sqrt(x) - \frac{1}{2}sqrt(x)^{2} + sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16}) - sqrt(x) - \frac{1}{2}\right)}{dx}\\=&\frac{(\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}sqrt(x)}{(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} + \frac{sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})*\frac{1}{2}}{(x)^{\frac{1}{2}}} - \frac{\frac{1}{2}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + \frac{(\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}}{(x)^{\frac{1}{2}}} + 0\\=&\frac{sqrt(x)}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} + \frac{sqrt(x)}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}} + \frac{sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})}{2x^{\frac{1}{2}}} + \frac{1}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}} + \frac{1}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} - \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sqrt(x)}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} + \frac{sqrt(x)}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}} + \frac{sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})}{2x^{\frac{1}{2}}} + \frac{1}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}} + \frac{1}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} - \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2}\right)}{dx}\\=&\frac{(\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}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}})sqrt(x)}{8} + \frac{\frac{1}{2}}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}(x)^{\frac{1}{2}}} + \frac{(\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}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}})sqrt(x)}{8x^{\frac{1}{2}}} + \frac{\frac{-1}{2}sqrt(x)}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{3}{2}}} + \frac{\frac{1}{2}}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}(x)^{\frac{1}{2}}} + \frac{\frac{-1}{2}sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})}{2x^{\frac{3}{2}}} + \frac{(\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}}{2x^{\frac{1}{2}}(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}} + \frac{(\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}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}})}{8x^{\frac{1}{2}}} + \frac{\frac{-1}{2}}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{3}{2}}} + \frac{(\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}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}})}{8} - \frac{\frac{-1}{2}}{2x^{\frac{3}{2}}} + 0\\=&\frac{-sqrt(x)}{64(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}} - \frac{sqrt(x)}{32(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}x^{\frac{1}{2}}} - \frac{sqrt(x)}{64(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}x} - \frac{sqrt(x)}{16(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{3}{2}}} + \frac{1}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x} + \frac{1}{8(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{1}{2}}x^{\frac{1}{2}}} - \frac{sqrt(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})}{4x^{\frac{3}{2}}} - \frac{1}{64(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}x} - \frac{1}{32(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{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{3}{2}}} - \frac{1}{64(\frac{1}{4}sqrt(x)^{2} + \frac{1}{2}sqrt(x) + \frac{13}{16})^{\frac{3}{2}}} + \frac{1}{4x^{\frac{3}{2}}}\\ \end{split}\end{equation} \]
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