There are 1 questions in this calculation: for each question, the 15 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ \frac{{x}^{100}}{(x - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{100}}{(x - 1)}\\\\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{-1307674368000x^{100}}{(x - 1)^{16}} + \frac{130767436800000x^{99}}{(x - 1)^{15}} - \frac{6472988121600000x^{98}}{(x - 1)^{14}} + \frac{211450945305600000x^{97}}{(x - 1)^{13}} - \frac{5127685423660800000x^{96}}{(x - 1)^{12}} + \frac{6217839765739601920x^{95}}{(x - 1)^{11}} + \frac{9156877472428687360x^{94}}{(x - 1)^{10}} - \frac{4377571298766684160x^{93}}{(x - 1)^{9}} + \frac{7078249173102518272x^{92}}{(x - 1)^{8}} - \frac{6767012618525114368x^{91}}{(x - 1)^{7}} - \frac{8517812651517755392x^{90}}{(x - 1)^{6}} + \frac{4289101796538679296x^{89}}{(x - 1)^{5}} + \frac{470963804663177216x^{88}}{(x - 1)^{4}} - \frac{4607042991082242048x^{87}}{(x - 1)^{3}} + \frac{6229863640792334336x^{86}}{(x - 1)^{2}} + \frac{2405386211790356480x^{85}}{(x - 1)}\\ \end{split}\end{equation} \]

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