There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ x(x - 9){(x - 9)}^{10000}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x - 9)^{10000}x^{2} - 9(x - 9)^{10000}x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x - 9)^{10000}x^{2} - 9(x - 9)^{10000}x\right)}{dx}\\=&(10000(x - 9)^{9999}(1 + 0))x^{2} + (x - 9)^{10000}*2x - 9(10000(x - 9)^{9999}(1 + 0))x - 9(x - 9)^{10000}\\=&10000(x - 9)^{9999}x^{2} + 2(x - 9)^{10000}x - 90000(x - 9)^{9999}x - 9(x - 9)^{10000}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 10000(x - 9)^{9999}x^{2} + 2(x - 9)^{10000}x - 90000(x - 9)^{9999}x - 9(x - 9)^{10000}\right)}{dx}\\=&10000(9999(x - 9)^{9998}(1 + 0))x^{2} + 10000(x - 9)^{9999}*2x + 2(10000(x - 9)^{9999}(1 + 0))x + 2(x - 9)^{10000} - 90000(9999(x - 9)^{9998}(1 + 0))x - 90000(x - 9)^{9999} - 9(10000(x - 9)^{9999}(1 + 0))\\=&99990000(x - 9)^{9998}x^{2} + 40000(x - 9)^{9999}x - 899910000(x - 9)^{9998}x + 2(x - 9)^{10000} - 180000(x - 9)^{9999}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 99990000(x - 9)^{9998}x^{2} + 40000(x - 9)^{9999}x - 899910000(x - 9)^{9998}x + 2(x - 9)^{10000} - 180000(x - 9)^{9999}\right)}{dx}\\=&99990000(9998(x - 9)^{9997}(1 + 0))x^{2} + 99990000(x - 9)^{9998}*2x + 40000(9999(x - 9)^{9998}(1 + 0))x + 40000(x - 9)^{9999} - 899910000(9998(x - 9)^{9997}(1 + 0))x - 899910000(x - 9)^{9998} + 2(10000(x - 9)^{9999}(1 + 0)) - 180000(9999(x - 9)^{9998}(1 + 0))\\=&999700020000(x - 9)^{9997}x^{2} + 599940000(x - 9)^{9998}x - 8997300180000(x - 9)^{9997}x + 60000(x - 9)^{9999} - 2699730000(x - 9)^{9998}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 999700020000(x - 9)^{9997}x^{2} + 599940000(x - 9)^{9998}x - 8997300180000(x - 9)^{9997}x + 60000(x - 9)^{9999} - 2699730000(x - 9)^{9998}\right)}{dx}\\=&999700020000(9997(x - 9)^{9996}(1 + 0))x^{2} + 999700020000(x - 9)^{9997}*2x + 599940000(9998(x - 9)^{9997}(1 + 0))x + 599940000(x - 9)^{9998} - 8997300180000(9997(x - 9)^{9996}(1 + 0))x - 8997300180000(x - 9)^{9997} + 60000(9999(x - 9)^{9998}(1 + 0)) - 2699730000(9998(x - 9)^{9997}(1 + 0))\\=&9994001099940000(x - 9)^{9996}x^{2} + 7997600160000(x - 9)^{9997}x - 89946009899460000(x - 9)^{9996}x + 1199880000(x - 9)^{9998} - 35989200720000(x - 9)^{9997}\\ \end{split}\end{equation} \]

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