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

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