There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(2aktN)sqrt(\frac{qx}{(kt)} + {n}^{2}{\frac{1}{N}}^{2}e^{\frac{qx}{(kt)}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(2aktN)sqrt(\frac{qx}{kt} + \frac{n^{2}e^{\frac{qx}{kt}}}{N^{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(2aktN)sqrt(\frac{qx}{kt} + \frac{n^{2}e^{\frac{qx}{kt}}}{N^{2}})\right)}{dx}\\=&\frac{0*\frac{1}{2}sqrt(\frac{qx}{kt} + \frac{n^{2}e^{\frac{qx}{kt}}}{N^{2}})}{(2aktN)^{\frac{1}{2}}} + \frac{sqrt(2aktN)(\frac{q}{kt} + \frac{n^{2}e^{\frac{qx}{kt}}q}{N^{2}kt})*\frac{1}{2}}{(\frac{qx}{kt} + \frac{n^{2}e^{\frac{qx}{kt}}}{N^{2}})^{\frac{1}{2}}}\\=&\frac{qsqrt(2aktN)}{2(\frac{qx}{kt} + \frac{n^{2}e^{\frac{qx}{kt}}}{N^{2}})^{\frac{1}{2}}kt} + \frac{qn^{2}e^{\frac{qx}{kt}}sqrt(2aktN)}{2(\frac{qx}{kt} + \frac{n^{2}e^{\frac{qx}{kt}}}{N^{2}})^{\frac{1}{2}}ktN^{2}}\\ \end{split}\end{equation} \]

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