There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ sqrt(1 - 2x + {x}^{3})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(-2x + x^{3} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(-2x + x^{3} + 1)\right)}{dx}\\=&\frac{(-2 + 3x^{2} + 0)*\frac{1}{2}}{(-2x + x^{3} + 1)^{\frac{1}{2}}}\\=&\frac{3x^{2}}{2(-2x + x^{3} + 1)^{\frac{1}{2}}} - \frac{1}{(-2x + x^{3} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{2}}{2(-2x + x^{3} + 1)^{\frac{1}{2}}} - \frac{1}{(-2x + x^{3} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{3(\frac{\frac{-1}{2}(-2 + 3x^{2} + 0)}{(-2x + x^{3} + 1)^{\frac{3}{2}}})x^{2}}{2} + \frac{3*2x}{2(-2x + x^{3} + 1)^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(-2 + 3x^{2} + 0)}{(-2x + x^{3} + 1)^{\frac{3}{2}}})\\=&\frac{-9x^{4}}{4(-2x + x^{3} + 1)^{\frac{3}{2}}} + \frac{3x^{2}}{(-2x + x^{3} + 1)^{\frac{3}{2}}} + \frac{3x}{(-2x + x^{3} + 1)^{\frac{1}{2}}} - \frac{1}{(-2x + x^{3} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-9x^{4}}{4(-2x + x^{3} + 1)^{\frac{3}{2}}} + \frac{3x^{2}}{(-2x + x^{3} + 1)^{\frac{3}{2}}} + \frac{3x}{(-2x + x^{3} + 1)^{\frac{1}{2}}} - \frac{1}{(-2x + x^{3} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-9(\frac{\frac{-3}{2}(-2 + 3x^{2} + 0)}{(-2x + x^{3} + 1)^{\frac{5}{2}}})x^{4}}{4} - \frac{9*4x^{3}}{4(-2x + x^{3} + 1)^{\frac{3}{2}}} + 3(\frac{\frac{-3}{2}(-2 + 3x^{2} + 0)}{(-2x + x^{3} + 1)^{\frac{5}{2}}})x^{2} + \frac{3*2x}{(-2x + x^{3} + 1)^{\frac{3}{2}}} + 3(\frac{\frac{-1}{2}(-2 + 3x^{2} + 0)}{(-2x + x^{3} + 1)^{\frac{3}{2}}})x + \frac{3}{(-2x + x^{3} + 1)^{\frac{1}{2}}} - (\frac{\frac{-3}{2}(-2 + 3x^{2} + 0)}{(-2x + x^{3} + 1)^{\frac{5}{2}}})\\=&\frac{81x^{6}}{8(-2x + x^{3} + 1)^{\frac{5}{2}}} - \frac{81x^{4}}{4(-2x + x^{3} + 1)^{\frac{5}{2}}} - \frac{27x^{3}}{2(-2x + x^{3} + 1)^{\frac{3}{2}}} + \frac{27x^{2}}{2(-2x + x^{3} + 1)^{\frac{5}{2}}} + \frac{9x}{(-2x + x^{3} + 1)^{\frac{3}{2}}} + \frac{3}{(-2x + x^{3} + 1)^{\frac{1}{2}}} - \frac{3}{(-2x + x^{3} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]

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