There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arcsin(\frac{rsin(wt)}{sqrt({r}^{2} + {h}^{2} + 2rhcos(wt))})\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(\frac{rsin(wt)}{sqrt(2rhcos(wt) + h^{2} + r^{2})})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(\frac{rsin(wt)}{sqrt(2rhcos(wt) + h^{2} + r^{2})})\right)}{dt}\\=&(\frac{(\frac{rcos(wt)w}{sqrt(2rhcos(wt) + h^{2} + r^{2})} + \frac{rsin(wt)*-(2rh*-sin(wt)w + 0 + 0)*\frac{1}{2}}{(2rhcos(wt) + h^{2} + r^{2})(2rhcos(wt) + h^{2} + r^{2})^{\frac{1}{2}}})}{((1 - (\frac{rsin(wt)}{sqrt(2rhcos(wt) + h^{2} + r^{2})})^{2})^{\frac{1}{2}})})\\=&\frac{rwcos(wt)}{(\frac{-r^{2}sin^{2}(wt)}{sqrt(2rhcos(wt) + h^{2} + r^{2})^{2}} + 1)^{\frac{1}{2}}sqrt(2rhcos(wt) + h^{2} + r^{2})} + \frac{r^{2}whsin^{2}(wt)}{(\frac{-r^{2}sin^{2}(wt)}{sqrt(2rhcos(wt) + h^{2} + r^{2})^{2}} + 1)^{\frac{1}{2}}(2rhcos(wt) + h^{2} + r^{2})^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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