There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {(16x + 1)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (16x + 1)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (16x + 1)^{\frac{1}{2}}\right)}{dx}\\=&(\frac{\frac{1}{2}(16 + 0)}{(16x + 1)^{\frac{1}{2}}})\\=&\frac{8}{(16x + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{8}{(16x + 1)^{\frac{1}{2}}}\right)}{dx}\\=&8(\frac{\frac{-1}{2}(16 + 0)}{(16x + 1)^{\frac{3}{2}}})\\=&\frac{-64}{(16x + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-64}{(16x + 1)^{\frac{3}{2}}}\right)}{dx}\\=&-64(\frac{\frac{-3}{2}(16 + 0)}{(16x + 1)^{\frac{5}{2}}})\\=&\frac{1536}{(16x + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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