There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {(4x + 1)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (4x + 1)^{\frac{1}{2}}\right)}{dx}\\=&((4x + 1)^{\frac{1}{2}}((0)ln(4x + 1) + \frac{(\frac{1}{2})(4 + 0)}{(4x + 1)}))\\=&\frac{2(4x + 1)^{\frac{1}{2}}}{(4x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2(4x + 1)^{\frac{1}{2}}}{(4x + 1)}\right)}{dx}\\=&\frac{2(\frac{\frac{1}{2}(4 + 0)}{(4x + 1)^{\frac{1}{2}}})}{(4x + 1)} + 2(4x + 1)^{\frac{1}{2}}(\frac{-(4 + 0)}{(4x + 1)^{2}})\\=&\frac{-4}{(4x + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4}{(4x + 1)^{\frac{3}{2}}}\right)}{dx}\\=&-4(\frac{\frac{-3}{2}(4 + 0)}{(4x + 1)^{\frac{5}{2}}})\\=&\frac{24}{(4x + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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