There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(\frac{1}{3})}{x} - \frac{{((\frac{1}{9}) - (\frac{x}{36}))}^{\frac{1}{2}}}{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{3}}{x} - \frac{(\frac{-1}{36}x + \frac{1}{9})^{\frac{1}{2}}}{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{3}}{x} - \frac{(\frac{-1}{36}x + \frac{1}{9})^{\frac{1}{2}}}{x}\right)}{dx}\\=&\frac{\frac{1}{3}*-1}{x^{2}} - \frac{(\frac{\frac{1}{2}(\frac{-1}{36} + 0)}{(\frac{-1}{36}x + \frac{1}{9})^{\frac{1}{2}}})}{x} - \frac{(\frac{-1}{36}x + \frac{1}{9})^{\frac{1}{2}}*-1}{x^{2}}\\=&\frac{-1}{3x^{2}} + \frac{1}{72(\frac{-1}{36}x + \frac{1}{9})^{\frac{1}{2}}x} + \frac{(\frac{-1}{36}x + \frac{1}{9})^{\frac{1}{2}}}{x^{2}}\\ \end{split}\end{equation} \]

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