There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (2x + 3){\frac{1}{(4x - 1)}}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x{\frac{1}{(4x - 1)}}^{\frac{1}{2}} + 3{\frac{1}{(4x - 1)}}^{\frac{1}{2}}\right)}{dx}\\=&2{\frac{1}{(4x - 1)}}^{\frac{1}{2}} + 2x({\frac{1}{(4x - 1)}}^{\frac{1}{2}}((0)ln(\frac{1}{(4x - 1)}) + \frac{(\frac{1}{2})((\frac{-(4 + 0)}{(4x - 1)^{2}}))}{(\frac{1}{(4x - 1)})})) + 3({\frac{1}{(4x - 1)}}^{\frac{1}{2}}((0)ln(\frac{1}{(4x - 1)}) + \frac{(\frac{1}{2})((\frac{-(4 + 0)}{(4x - 1)^{2}}))}{(\frac{1}{(4x - 1)})}))\\=&\frac{-4x}{(4x - 1)^{\frac{3}{2}}} - \frac{6}{(4x - 1)^{\frac{3}{2}}} + \frac{2}{(4x - 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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