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。
\[ \begin{equation}\begin{split}【1/1】求函数arcsin(\frac{rsin(wt)}{sqrt({r}^{2} + {h}^{2} + 2rhcos(w)t)}) 关于 t 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arcsin(\frac{rsin(wt)}{sqrt(2rhtcos(w) + h^{2} + r^{2})})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin(\frac{rsin(wt)}{sqrt(2rhtcos(w) + h^{2} + r^{2})})\right)}{dt}\\=&(\frac{(\frac{rcos(wt)w}{sqrt(2rhtcos(w) + h^{2} + r^{2})} + \frac{rsin(wt)*-(2rhcos(w) + 2rht*-sin(w)*0 + 0 + 0)*\frac{1}{2}}{(2rhtcos(w) + h^{2} + r^{2})(2rhtcos(w) + h^{2} + r^{2})^{\frac{1}{2}}})}{((1 - (\frac{rsin(wt)}{sqrt(2rhtcos(w) + h^{2} + r^{2})})^{2})^{\frac{1}{2}})})\\=&\frac{rwcos(wt)}{(\frac{-r^{2}sin^{2}(wt)}{sqrt(2rhtcos(w) + h^{2} + r^{2})^{2}} + 1)^{\frac{1}{2}}sqrt(2rhtcos(w) + h^{2} + r^{2})} - \frac{r^{2}hsin(wt)cos(w)}{(\frac{-r^{2}sin^{2}(wt)}{sqrt(2rhtcos(w) + h^{2} + r^{2})^{2}} + 1)^{\frac{1}{2}}(2rhtcos(w) + h^{2} + r^{2})^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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