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

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