There are 1 questions in this calculation: for each question, the 15 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ \frac{({x}^{100}ln(x))}{({e}^{x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{100}{e}^{(-x)}ln(x)\\\\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&2405386211790356480x^{85}{e}^{(-x)}ln(x) + 6229863640792334336x^{86}{e}^{(-x)}ln(x) + 6919850541313654784x^{87}{e}^{(-x)}ln(x) - 6070420723792654336x^{88}{e}^{(-x)}ln(x) + 2484555584069472256x^{89}{e}^{(-x)}ln(x) + 1005078298870409216x^{90}{e}^{(-x)}ln(x) + 5319660770434807808x^{91}{e}^{(-x)}ln(x) + 7058016036366094848x^{92}{e}^{(-x)}ln(x) + 519163614889920000x^{93}{e}^{(-x)}ln(x) - 4295680028640000x^{94}{e}^{(-x)}ln(x) + 27130610707200x^{95}{e}^{(-x)}ln(x) - 128459331000x^{96}{e}^{(-x)}ln(x) + 441441000x^{97}{e}^{(-x)}ln(x) - 1039500x^{98}{e}^{(-x)}ln(x) + 1500x^{99}{e}^{(-x)}ln(x) - x^{100}{e}^{(-x)}ln(x) - 4146746573668538368x^{85}{e}^{(-x)} + 37481354847565200x^{93}{e}^{(-x)} + 8615746393694828928x^{89}{e}^{(-x)} - 264430689923400x^{94}{e}^{(-x)} + 8312375295529616384x^{87}{e}^{(-x)} + 1384503192072x^{95}{e}^{(-x)} + 4615371553050515392x^{90}{e}^{(-x)} - 5217294810x^{96}{e}^{(-x)} + 9016213416731491328x^{86}{e}^{(-x)} + 13377910x^{97}{e}^{(-x)} - 7913594903125111488x^{91}{e}^{(-x)} - 20895x^{98}{e}^{(-x)} + 7974670182200490880x^{88}{e}^{(-x)} - 4004929615713483600x^{92}{e}^{(-x)} + 15x^{99}{e}^{(-x)}\\ \end{split}\end{equation} \]

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