There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt((\frac{x}{2})th(\frac{1}{x}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{1}{2}xth(\frac{1}{x}))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{1}{2}xth(\frac{1}{x}))\right)}{dx}\\=&\frac{(\frac{1}{2}th(\frac{1}{x}) + \frac{\frac{1}{2}x(1 - th^{2}(\frac{1}{x}))*-1}{x^{2}})*\frac{1}{2}}{(\frac{1}{2}xth(\frac{1}{x}))^{\frac{1}{2}}}\\=&\frac{2^{\frac{1}{2}}th^{\frac{1}{2}}(\frac{1}{x})}{4x^{\frac{1}{2}}} - \frac{2^{\frac{1}{2}}}{4x^{\frac{3}{2}}th^{\frac{1}{2}}(\frac{1}{x})} + \frac{2^{\frac{1}{2}}th^{\frac{3}{2}}(\frac{1}{x})}{4x^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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