There are 1 questions in this calculation: for each question, the 6 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 6th\ derivative\ of\ function\ \frac{{x}^{6}}{(x + {x}^{2} + {x}^{3} + {x}^{4} + {x}^{5})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})}\\\\ &\color{blue}{The\ 6th\ derivative\ of\ function:} \\=&\frac{8621280x^{12}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{21150720x^{13}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{46668960x^{14}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{93412800x^{15}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{12068640x^{10}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{170609760x^{16}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{30650400x^{11}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{285491520x^{17}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{68673600x^{12}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{438760080x^{18}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{137412000x^{13}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{619755840x^{19}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{6811200x^{8}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{246985200x^{14}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{804276000x^{20}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{18115200x^{9}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{400379760x^{15}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{957300480x^{21}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{1041478560x^{22}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{41257440x^{10}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{586720800x^{16}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{1029983040x^{23}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{776779200x^{17}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{919113120x^{24}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{81956160x^{11}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{1928160x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} - \frac{925380000x^{18}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{731678400x^{25}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{143434800x^{12}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{5533920x^{7}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} - \frac{987386400x^{19}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{510570000x^{26}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{304200000x^{27}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{220492800x^{13}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{12830400x^{8}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} - \frac{935297280x^{20}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{148500000x^{28}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{298404000x^{14}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{773892000x^{21}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{54000000x^{29}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{545490000x^{22}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{11250000x^{30}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{3119040x^{11}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{354674880x^{15}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{24840000x^{9}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{284400x^{4}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{317250000x^{23}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{982800x^{10}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{365224320x^{16}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{41089680x^{10}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{859680x^{5}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{139500000x^{24}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{262080x^{9}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{56160x^{8}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} + \frac{316857600x^{17}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{57950640x^{11}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{2190960x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{36000000x^{25}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} - \frac{4118400x^{9}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} - \frac{1188000x^{8}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{228240000x^{18}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{66224880x^{12}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} - \frac{277200x^{7}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{8640x^{7}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{46800x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{126720000x^{19}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} + \frac{42750000x^{20}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{62910000x^{13}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{3816000x^{7}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{19440x^{2}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} + \frac{2145600x^{7}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} + \frac{551520x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{47250000x^{14}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{5400000x^{8}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{59760x^{3}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} + \frac{103680x^{5}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{22770000x^{15}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} - \frac{555120x^{5}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{6240960x^{9}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{150480x^{4}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} - \frac{118800x^{4}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{5101200x^{10}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} + \frac{72000x^{3}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{331920x^{5}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} + \frac{720x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{7}} - \frac{4320x^{5}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{6}} + \frac{10800x^{4}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{5}} - \frac{14400x^{3}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{4}} + \frac{10800x^{2}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{3}} - \frac{4320x}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} + \frac{720}{(x + x^{2} + x^{3} + x^{4} + x^{5})}\\ \end{split}\end{equation} \]

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