There are 1 questions in this calculation: for each question, the 1 derivative of k is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(\frac{(bs + m(n + k + t) + ms - 1)}{(mbs(n + k + t))})\ with\ respect\ to\ k：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})\right)}{dk}\\=&\frac{((\frac{-(0 + bsm + 0)}{(bsmn + bsmk + bsmt)^{2}})bs + 0 + (\frac{-(0 + bsm + 0)}{(bsmn + bsmk + bsmt)^{2}})mn + 0 + (\frac{-(0 + bsm + 0)}{(bsmn + bsmk + bsmt)^{2}})mk + \frac{m}{(bsmn + bsmk + bsmt)} + (\frac{-(0 + bsm + 0)}{(bsmn + bsmk + bsmt)^{2}})mt + 0 + (\frac{-(0 + bsm + 0)}{(bsmn + bsmk + bsmt)^{2}})sm + 0 - (\frac{-(0 + bsm + 0)}{(bsmn + bsmk + bsmt)^{2}}))*\frac{1}{2}}{(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}}\\=&\frac{-bsm^{2}n}{2(bsmn + bsmk + bsmt)^{2}(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}} - \frac{bsm^{2}k}{2(bsmn + bsmk + bsmt)^{2}(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}} - \frac{bsm^{2}t}{2(bsmn + bsmk + bsmt)^{2}(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}} + \frac{m}{2(bsmn + bsmk + bsmt)(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}} - \frac{b^{2}s^{2}m}{2(bsmn + bsmk + bsmt)^{2}(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}} - \frac{bs^{2}m^{2}}{2(bsmn + bsmk + bsmt)^{2}(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}} + \frac{bsm}{2(bsmn + bsmk + bsmt)^{2}(\frac{bs}{(bsmn + bsmk + bsmt)} + \frac{mn}{(bsmn + bsmk + bsmt)} + \frac{mk}{(bsmn + bsmk + bsmt)} + \frac{mt}{(bsmn + bsmk + bsmt)} + \frac{sm}{(bsmn + bsmk + bsmt)} - \frac{1}{(bsmn + bsmk + bsmt)})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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