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

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