There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {x}^{2}({e}^{x}x - 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3}{e}^{x} - x^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3}{e}^{x} - x^{2}\right)}{dx}\\=&3x^{2}{e}^{x} + x^{3}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 2x\\=&3x^{2}{e}^{x} + x^{3}{e}^{x} - 2x\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3x^{2}{e}^{x} + x^{3}{e}^{x} - 2x\right)}{dx}\\=&3*2x{e}^{x} + 3x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 3x^{2}{e}^{x} + x^{3}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) - 2\\=&6x{e}^{x} + 6x^{2}{e}^{x} + x^{3}{e}^{x} - 2\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 6x{e}^{x} + 6x^{2}{e}^{x} + x^{3}{e}^{x} - 2\right)}{dx}\\=&6{e}^{x} + 6x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 6*2x{e}^{x} + 6x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 3x^{2}{e}^{x} + x^{3}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0\\=&6{e}^{x} + 18x{e}^{x} + 9x^{2}{e}^{x} + x^{3}{e}^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 6{e}^{x} + 18x{e}^{x} + 9x^{2}{e}^{x} + x^{3}{e}^{x}\right)}{dx}\\=&6({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 18{e}^{x} + 18x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 9*2x{e}^{x} + 9x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 3x^{2}{e}^{x} + x^{3}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&24{e}^{x} + 36x{e}^{x} + 12x^{2}{e}^{x} + x^{3}{e}^{x}\\ \end{split}\end{equation} \]

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