There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ 16{(1 - \frac{({(x)}^{2})}{9})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 16(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 16(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}\right)}{dx}\\=&16(\frac{\frac{1}{2}(\frac{-1}{9}*2x + 0)}{(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}})\\=&\frac{-16x}{9(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-16x}{9(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{-16(\frac{\frac{-1}{2}(\frac{-1}{9}*2x + 0)}{(\frac{-1}{9}x^{2} + 1)^{\frac{3}{2}}})x}{9} - \frac{16}{9(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-16x^{2}}{81(\frac{-1}{9}x^{2} + 1)^{\frac{3}{2}}} - \frac{16}{9(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-16x^{2}}{81(\frac{-1}{9}x^{2} + 1)^{\frac{3}{2}}} - \frac{16}{9(\frac{-1}{9}x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{-16(\frac{\frac{-3}{2}(\frac{-1}{9}*2x + 0)}{(\frac{-1}{9}x^{2} + 1)^{\frac{5}{2}}})x^{2}}{81} - \frac{16*2x}{81(\frac{-1}{9}x^{2} + 1)^{\frac{3}{2}}} - \frac{16(\frac{\frac{-1}{2}(\frac{-1}{9}*2x + 0)}{(\frac{-1}{9}x^{2} + 1)^{\frac{3}{2}}})}{9}\\=&\frac{-16x^{3}}{243(\frac{-1}{9}x^{2} + 1)^{\frac{5}{2}}} - \frac{16x}{27(\frac{-1}{9}x^{2} + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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