There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {(1 - 3x + {x}^{2})}^{\frac{1}{3}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (-3x + x^{2} + 1)^{\frac{1}{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (-3x + x^{2} + 1)^{\frac{1}{3}}\right)}{dx}\\=&(\frac{\frac{1}{3}(-3 + 2x + 0)}{(-3x + x^{2} + 1)^{\frac{2}{3}}})\\=&\frac{2x}{3(-3x + x^{2} + 1)^{\frac{2}{3}}} - \frac{1}{(-3x + x^{2} + 1)^{\frac{2}{3}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x}{3(-3x + x^{2} + 1)^{\frac{2}{3}}} - \frac{1}{(-3x + x^{2} + 1)^{\frac{2}{3}}}\right)}{dx}\\=&\frac{2(\frac{\frac{-2}{3}(-3 + 2x + 0)}{(-3x + x^{2} + 1)^{\frac{5}{3}}})x}{3} + \frac{2}{3(-3x + x^{2} + 1)^{\frac{2}{3}}} - (\frac{\frac{-2}{3}(-3 + 2x + 0)}{(-3x + x^{2} + 1)^{\frac{5}{3}}})\\=&\frac{-8x^{2}}{9(-3x + x^{2} + 1)^{\frac{5}{3}}} + \frac{8x}{3(-3x + x^{2} + 1)^{\frac{5}{3}}} - \frac{2}{(-3x + x^{2} + 1)^{\frac{5}{3}}} + \frac{2}{3(-3x + x^{2} + 1)^{\frac{2}{3}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-8x^{2}}{9(-3x + x^{2} + 1)^{\frac{5}{3}}} + \frac{8x}{3(-3x + x^{2} + 1)^{\frac{5}{3}}} - \frac{2}{(-3x + x^{2} + 1)^{\frac{5}{3}}} + \frac{2}{3(-3x + x^{2} + 1)^{\frac{2}{3}}}\right)}{dx}\\=&\frac{-8(\frac{\frac{-5}{3}(-3 + 2x + 0)}{(-3x + x^{2} + 1)^{\frac{8}{3}}})x^{2}}{9} - \frac{8*2x}{9(-3x + x^{2} + 1)^{\frac{5}{3}}} + \frac{8(\frac{\frac{-5}{3}(-3 + 2x + 0)}{(-3x + x^{2} + 1)^{\frac{8}{3}}})x}{3} + \frac{8}{3(-3x + x^{2} + 1)^{\frac{5}{3}}} - 2(\frac{\frac{-5}{3}(-3 + 2x + 0)}{(-3x + x^{2} + 1)^{\frac{8}{3}}}) + \frac{2(\frac{\frac{-2}{3}(-3 + 2x + 0)}{(-3x + x^{2} + 1)^{\frac{5}{3}}})}{3}\\=&\frac{80x^{3}}{27(-3x + x^{2} + 1)^{\frac{8}{3}}} - \frac{40x^{2}}{3(-3x + x^{2} + 1)^{\frac{8}{3}}} - \frac{8x}{3(-3x + x^{2} + 1)^{\frac{5}{3}}} + \frac{20x}{(-3x + x^{2} + 1)^{\frac{8}{3}}} + \frac{4}{(-3x + x^{2} + 1)^{\frac{5}{3}}} - \frac{10}{(-3x + x^{2} + 1)^{\frac{8}{3}}}\\ \end{split}\end{equation} \]

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