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 t 求 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(1 - S{(\frac{L}{t})}^{\frac{1}{2}}){(Lt)}^{\frac{1}{2}}{(1 - {({(\frac{t}{L})}^{\frac{1}{2}} - S)}^{2})}^{\frac{1}{2}} + (1 - S{(Lt)}^{\frac{1}{2}}){(\frac{L}{t})}^{\frac{1}{2}}{(1 - {({(\frac{1}{(Lt)})}^{\frac{1}{2}} - S)}^{2})}^{\frac{1}{2}} 关于 t 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}t^{\frac{1}{2}} - (\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}SL + \frac{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}}{t^{\frac{1}{2}}} - (\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}SL\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( (\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}t^{\frac{1}{2}} - (\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}SL + \frac{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}}{t^{\frac{1}{2}}} - (\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}SL\right)}{dt}\\=&(\frac{\frac{1}{2}(\frac{-1}{L} + \frac{2S*\frac{1}{2}}{L^{\frac{1}{2}}t^{\frac{1}{2}}} + 0 + 0)}{(\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}})L^{\frac{1}{2}}t^{\frac{1}{2}} + \frac{(\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}*\frac{1}{2}}{t^{\frac{1}{2}}} - (\frac{\frac{1}{2}(\frac{-1}{L} + \frac{2S*\frac{1}{2}}{L^{\frac{1}{2}}t^{\frac{1}{2}}} + 0 + 0)}{(\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}})SL + 0 + \frac{(\frac{\frac{1}{2}(\frac{--1}{Lt^{2}} + \frac{2S*\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0 + 0)}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}})L^{\frac{1}{2}}}{t^{\frac{1}{2}}} + \frac{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}*\frac{-1}{2}}{t^{\frac{3}{2}}} - (\frac{\frac{1}{2}(\frac{--1}{Lt^{2}} + \frac{2S*\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0 + 0)}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}})SL + 0\\=&\frac{1}{2(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}t^{\frac{5}{2}}} - \frac{S}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}t^{2}} + \frac{(\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}}{2t^{\frac{1}{2}}} - \frac{S^{2}L^{\frac{1}{2}}}{2(\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}t^{\frac{1}{2}}} + \frac{S^{2}L^{\frac{1}{2}}}{2(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}t^{\frac{3}{2}}} - \frac{t^{\frac{1}{2}}}{2(\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}} - \frac{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}L^{\frac{1}{2}}}{2t^{\frac{3}{2}}} + \frac{S}{(\frac{-t}{L} + \frac{2St^{\frac{1}{2}}}{L^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]