There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ 6{(576x + 1)}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 6(576x + 1)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 6(576x + 1)^{\frac{1}{2}}\right)}{dx}\\=&6(\frac{\frac{1}{2}(576 + 0)}{(576x + 1)^{\frac{1}{2}}})\\=&\frac{1728}{(576x + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1728}{(576x + 1)^{\frac{1}{2}}}\right)}{dx}\\=&1728(\frac{\frac{-1}{2}(576 + 0)}{(576x + 1)^{\frac{3}{2}}})\\=&\frac{-497664}{(576x + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-497664}{(576x + 1)^{\frac{3}{2}}}\right)}{dx}\\=&-497664(\frac{\frac{-3}{2}(576 + 0)}{(576x + 1)^{\frac{5}{2}}})\\=&\frac{429981696}{(576x + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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