There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ ({x}^{2}){(a - x)}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = a^{4}x^{2} - 4a^{3}x^{3} + 6a^{2}x^{4} - 4ax^{5} + x^{6}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( a^{4}x^{2} - 4a^{3}x^{3} + 6a^{2}x^{4} - 4ax^{5} + x^{6}\right)}{dx}\\=&a^{4}*2x - 4a^{3}*3x^{2} + 6a^{2}*4x^{3} - 4a*5x^{4} + 6x^{5}\\=&2a^{4}x - 12a^{3}x^{2} + 24a^{2}x^{3} - 20ax^{4} + 6x^{5}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2a^{4}x - 12a^{3}x^{2} + 24a^{2}x^{3} - 20ax^{4} + 6x^{5}\right)}{dx}\\=&2a^{4} - 12a^{3}*2x + 24a^{2}*3x^{2} - 20a*4x^{3} + 6*5x^{4}\\=& - 24a^{3}x + 72a^{2}x^{2} - 80ax^{3} + 2a^{4} + 30x^{4}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 24a^{3}x + 72a^{2}x^{2} - 80ax^{3} + 2a^{4} + 30x^{4}\right)}{dx}\\=& - 24a^{3} + 72a^{2}*2x - 80a*3x^{2} + 0 + 30*4x^{3}\\=&144a^{2}x - 240ax^{2} - 24a^{3} + 120x^{3}\\ \end{split}\end{equation} \]

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