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

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