There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ sqrt(2(2{x}^{2} + 10)) - 2x\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(4x^{2} + 20) - 2x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(4x^{2} + 20) - 2x\right)}{dx}\\=&\frac{(4*2x + 0)*\frac{1}{2}}{(4x^{2} + 20)^{\frac{1}{2}}} - 2\\=&\frac{4x}{(4x^{2} + 20)^{\frac{1}{2}}} - 2\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x}{(4x^{2} + 20)^{\frac{1}{2}}} - 2\right)}{dx}\\=&4(\frac{\frac{-1}{2}(4*2x + 0)}{(4x^{2} + 20)^{\frac{3}{2}}})x + \frac{4}{(4x^{2} + 20)^{\frac{1}{2}}} + 0\\=&\frac{-16x^{2}}{(4x^{2} + 20)^{\frac{3}{2}}} + \frac{4}{(4x^{2} + 20)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-16x^{2}}{(4x^{2} + 20)^{\frac{3}{2}}} + \frac{4}{(4x^{2} + 20)^{\frac{1}{2}}}\right)}{dx}\\=&-16(\frac{\frac{-3}{2}(4*2x + 0)}{(4x^{2} + 20)^{\frac{5}{2}}})x^{2} - \frac{16*2x}{(4x^{2} + 20)^{\frac{3}{2}}} + 4(\frac{\frac{-1}{2}(4*2x + 0)}{(4x^{2} + 20)^{\frac{3}{2}}})\\=&\frac{192x^{3}}{(4x^{2} + 20)^{\frac{5}{2}}} - \frac{48x}{(4x^{2} + 20)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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