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。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{2{(1 - S{(Lt)}^{\frac{1}{2}})}^{2}}{({P}^{2})t} + \frac{2(1 - S{(Lt)}^{\frac{1}{2}})(1 - S{(\frac{L}{t})}^{\frac{1}{2}})}{P} + L{\frac{1}{(P)}}^{2})(\frac{P}{2} - arcsin({(\frac{1}{(Lt)})}^{\frac{1}{2}} - S)) 关于 t 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{4SL^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t^{\frac{1}{2}}} - \frac{2S^{2}Larcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}} - \frac{2arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t} + \frac{2SL^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{Pt^{\frac{1}{2}}} + \frac{2SL^{\frac{1}{2}}t^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P} + \frac{1}{Pt} - \frac{2arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P} - \frac{SL^{\frac{1}{2}}}{t^{\frac{1}{2}}} - \frac{2SL^{\frac{1}{2}}}{Pt^{\frac{1}{2}}} - SL^{\frac{1}{2}}t^{\frac{1}{2}} - \frac{2S^{2}Larcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P} + S^{2}L + \frac{S^{2}L}{P} - \frac{Larcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}} + \frac{\frac{1}{2}L}{P} + 1\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{4SL^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t^{\frac{1}{2}}} - \frac{2S^{2}Larcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}} - \frac{2arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t} + \frac{2SL^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{Pt^{\frac{1}{2}}} + \frac{2SL^{\frac{1}{2}}t^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P} + \frac{1}{Pt} - \frac{2arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P} - \frac{SL^{\frac{1}{2}}}{t^{\frac{1}{2}}} - \frac{2SL^{\frac{1}{2}}}{Pt^{\frac{1}{2}}} - SL^{\frac{1}{2}}t^{\frac{1}{2}} - \frac{2S^{2}Larcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P} + S^{2}L + \frac{S^{2}L}{P} - \frac{Larcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}} + \frac{\frac{1}{2}L}{P} + 1\right)}{dt}\\=&\frac{4SL^{\frac{1}{2}}*\frac{-1}{2}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t^{\frac{3}{2}}} + \frac{4SL^{\frac{1}{2}}(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{P^{2}t^{\frac{1}{2}}} - \frac{2S^{2}L(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{P^{2}} - \frac{2*-arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t^{2}} - \frac{2(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{P^{2}t} + \frac{2SL^{\frac{1}{2}}*\frac{-1}{2}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{Pt^{\frac{3}{2}}} + \frac{2SL^{\frac{1}{2}}(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{Pt^{\frac{1}{2}}} + \frac{2SL^{\frac{1}{2}}*\frac{1}{2}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{Pt^{\frac{1}{2}}} + \frac{2SL^{\frac{1}{2}}t^{\frac{1}{2}}(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{P} + \frac{-1}{Pt^{2}} - \frac{2(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{P} - \frac{SL^{\frac{1}{2}}*\frac{-1}{2}}{t^{\frac{3}{2}}} - \frac{2SL^{\frac{1}{2}}*\frac{-1}{2}}{Pt^{\frac{3}{2}}} - \frac{SL^{\frac{1}{2}}*\frac{1}{2}}{t^{\frac{1}{2}}} - \frac{2S^{2}L(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{P} + 0 + 0 - \frac{L(\frac{(\frac{\frac{-1}{2}}{L^{\frac{1}{2}}t^{\frac{3}{2}}} + 0)}{((1 - (\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)^{2})^{\frac{1}{2}})})}{P^{2}} + 0 + 0\\=& - \frac{2SL^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t^{\frac{3}{2}}} - \frac{2S}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}P^{2}t^{2}} - \frac{S}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}Pt^{2}} + \frac{2arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{P^{2}t^{2}} + \frac{1}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}P^{2}L^{\frac{1}{2}}t^{\frac{5}{2}}} - \frac{SL^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{Pt^{\frac{3}{2}}} - \frac{S}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}Pt} + \frac{SL^{\frac{1}{2}}arcsin(\frac{1}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S)}{Pt^{\frac{1}{2}}} + \frac{S^{2}L^{\frac{1}{2}}}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}P^{2}t^{\frac{3}{2}}} - \frac{1}{Pt^{2}} + \frac{1}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}PL^{\frac{1}{2}}t^{\frac{3}{2}}} + \frac{SL^{\frac{1}{2}}}{2t^{\frac{3}{2}}} + \frac{SL^{\frac{1}{2}}}{Pt^{\frac{3}{2}}} - \frac{SL^{\frac{1}{2}}}{2t^{\frac{1}{2}}} + \frac{S^{2}L^{\frac{1}{2}}}{(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}Pt^{\frac{3}{2}}} + \frac{L^{\frac{1}{2}}}{2(\frac{-1}{Lt} + \frac{2S}{L^{\frac{1}{2}}t^{\frac{1}{2}}} - S^{2} + 1)^{\frac{1}{2}}P^{2}t^{\frac{3}{2}}}\\ \end{split}\end{equation} \]