There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(1 + \frac{\frac{1}{2}}{x})}^{\frac{1}{2}})}{(40 + 3x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(\frac{\frac{1}{2}}{x} + 1)^{\frac{1}{2}}}{(3x + 40)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(\frac{\frac{1}{2}}{x} + 1)^{\frac{1}{2}}}{(3x + 40)}\right)}{dx}\\=&\frac{(\frac{\frac{1}{2}(\frac{\frac{1}{2}*-1}{x^{2}} + 0)}{(\frac{\frac{1}{2}}{x} + 1)^{\frac{1}{2}}})}{(3x + 40)} + (\frac{\frac{1}{2}}{x} + 1)^{\frac{1}{2}}(\frac{-(3 + 0)}{(3x + 40)^{2}})\\=&\frac{-1}{4(\frac{\frac{1}{2}}{x} + 1)^{\frac{1}{2}}(3x + 40)x^{2}} - \frac{3(\frac{\frac{1}{2}}{x} + 1)^{\frac{1}{2}}}{(3x + 40)^{2}}\\ \end{split}\end{equation} \]

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