Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 15 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ arccot(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{1428329123020800x^{14}}{(x^{2} + 1)^{15}} + \frac{-663152807116800x^{12}}{(x^{2} + 1)^{14}} + \frac{-612141052723200x^{12}}{(x^{2} + 1)^{14}} + \frac{258982753075200x^{10}}{(x^{2} + 1)^{13}} + \frac{-561129298329600x^{12}}{(x^{2} + 1)^{14}} + \frac{237400856985600x^{10}}{(x^{2} + 1)^{13}} + \frac{431637921792000x^{10}}{(x^{2} + 1)^{13}} + \frac{-80932110336000x^{8}}{(x^{2} + 1)^{12}} + \frac{-510117543936000x^{12}}{(x^{2} + 1)^{14}} + \frac{196199055360000x^{10}}{(x^{2} + 1)^{13}} + \frac{-73574645760000x^{8}}{(x^{2} + 1)^{12}} + \frac{353158299648000x^{10}}{(x^{2} + 1)^{13}} + \frac{-132434362368000x^{8}}{(x^{2} + 1)^{12}} + \frac{-235438866432000x^{8}}{(x^{2} + 1)^{12}} + \frac{74912366592000x^{6}}{(x^{2} + 1)^{11}} + \frac{-459105789542400x^{12}}{(x^{2} + 1)^{14}} + \frac{194237064806400x^{10}}{(x^{2} + 1)^{13}} + \frac{158921234841600x^{10}}{(x^{2} + 1)^{13}} + \frac{-59595463065600x^{8}}{(x^{2} + 1)^{12}} + \frac{-211894979788800x^{8}}{(x^{2} + 1)^{12}} + \frac{16855282483200x^{6}}{(x^{2} + 1)^{11}} + \frac{282526639718400x^{10}}{(x^{2} + 1)^{13}} + \frac{-188351093145600x^{8}}{(x^{2} + 1)^{12}} + \frac{59929893273600x^{6}}{(x^{2} + 1)^{11}} + \frac{-164807206502400x^{8}}{(x^{2} + 1)^{12}} + \frac{52438656614400x^{6}}{(x^{2} + 1)^{11}} + \frac{44947419955200x^{6}}{(x^{2} + 1)^{11}} + \frac{-5618427494400x^{4}}{(x^{2} + 1)^{10}} + \frac{-408094035148800x^{12}}{(x^{2} + 1)^{14}} + \frac{172655168716800x^{10}}{(x^{2} + 1)^{13}} + \frac{313918488576000x^{10}}{(x^{2} + 1)^{13}} + \frac{251134790860800x^{10}}{(x^{2} + 1)^{13}} + \frac{-94175546572800x^{8}}{(x^{2} + 1)^{12}} + \frac{-83711596953600x^{8}}{(x^{2} + 1)^{12}} + \frac{26635508121600x^{6}}{(x^{2} + 1)^{11}} + \frac{-146495294668800x^{8}}{(x^{2} + 1)^{12}} + \frac{46612139212800x^{6}}{(x^{2} + 1)^{11}} + \frac{19976631091200x^{6}}{(x^{2} + 1)^{11}} + \frac{-4994157772800x^{4}}{(x^{2} + 1)^{10}} + \frac{219742942003200x^{10}}{(x^{2} + 1)^{13}} + \frac{-82403603251200x^{8}}{(x^{2} + 1)^{12}} + \frac{-64091691417600x^{8}}{(x^{2} + 1)^{12}} + \frac{20392810905600x^{6}}{(x^{2} + 1)^{11}} + \frac{69918208819200x^{6}}{(x^{2} + 1)^{11}} + \frac{-4369888051200x^{4}}{(x^{2} + 1)^{10}} + \frac{-109871471001600x^{8}}{(x^{2} + 1)^{12}} + \frac{29964946636800x^{6}}{(x^{2} + 1)^{11}} + \frac{-7491236659200x^{4}}{(x^{2} + 1)^{10}} + \frac{49941577728000x^{6}}{(x^{2} + 1)^{11}} + \frac{-6242697216000x^{4}}{(x^{2} + 1)^{10}} + \frac{-2497078886400x^{4}}{(x^{2} + 1)^{10}} + \frac{416179814400x^{2}}{(x^{2} + 1)^{9}} + \frac{-357082280755200x^{12}}{(x^{2} + 1)^{14}} + \frac{151073272627200x^{10}}{(x^{2} + 1)^{13}} + \frac{137339338752000x^{10}}{(x^{2} + 1)^{13}} + \frac{-51502252032000x^{8}}{(x^{2} + 1)^{12}} + \frac{123605404876800x^{10}}{(x^{2} + 1)^{13}} + \frac{-46352026828800x^{8}}{(x^{2} + 1)^{12}} + \frac{96137537126400x^{10}}{(x^{2} + 1)^{13}} + \frac{-36051576422400x^{8}}{(x^{2} + 1)^{12}} + \frac{-32045845708800x^{8}}{(x^{2} + 1)^{12}} + \frac{10196405452800x^{6}}{(x^{2} + 1)^{11}} + \frac{-28040114995200x^{8}}{(x^{2} + 1)^{12}} + \frac{8921854771200x^{6}}{(x^{2} + 1)^{11}} + \frac{30589216358400x^{6}}{(x^{2} + 1)^{11}} + \frac{-1911826022400x^{4}}{(x^{2} + 1)^{10}} + \frac{-24034384281600x^{8}}{(x^{2} + 1)^{12}} + \frac{6554832076800x^{6}}{(x^{2} + 1)^{11}} + \frac{-1638708019200x^{4}}{(x^{2} + 1)^{10}} + \frac{10924720128000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2731180032000x^{4}}{(x^{2} + 1)^{10}} + \frac{-2184944025600x^{4}}{(x^{2} + 1)^{10}} + \frac{182078668800x^{2}}{(x^{2} + 1)^{9}} + \frac{164807206502400x^{10}}{(x^{2} + 1)^{13}} + \frac{-61802702438400x^{8}}{(x^{2} + 1)^{12}} + \frac{-54935735500800x^{8}}{(x^{2} + 1)^{12}} + \frac{-48068768563200x^{8}}{(x^{2} + 1)^{12}} + \frac{13109664153600x^{6}}{(x^{2} + 1)^{11}} + \frac{-3277416038400x^{4}}{(x^{2} + 1)^{10}} + \frac{-2341011456000x^{4}}{(x^{2} + 1)^{10}} + \frac{-3745618329600x^{4}}{(x^{2} + 1)^{10}} + \frac{312134860800x^{2}}{(x^{2} + 1)^{9}} + \frac{-68669669376000x^{8}}{(x^{2} + 1)^{12}} + \frac{21849440256000x^{6}}{(x^{2} + 1)^{11}} + \frac{-4682022912000x^{4}}{(x^{2} + 1)^{10}} + \frac{15606743040000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1950842880000x^{4}}{(x^{2} + 1)^{10}} + \frac{-1560674304000x^{4}}{(x^{2} + 1)^{10}} + \frac{260112384000x^{2}}{(x^{2} + 1)^{9}} + \frac{-936404582400x^{4}}{(x^{2} + 1)^{10}} + \frac{156067430400x^{2}}{(x^{2} + 1)^{9}} + \frac{104044953600x^{2}}{(x^{2} + 1)^{9}} + \frac{-306070526361600x^{12}}{(x^{2} + 1)^{14}} + \frac{129491376537600x^{10}}{(x^{2} + 1)^{13}} + \frac{235438866432000x^{10}}{(x^{2} + 1)^{13}} + \frac{-88289574912000x^{8}}{(x^{2} + 1)^{12}} + \frac{105947489894400x^{10}}{(x^{2} + 1)^{13}} + \frac{-39730308710400x^{8}}{(x^{2} + 1)^{12}} + \frac{-141263319859200x^{8}}{(x^{2} + 1)^{12}} + \frac{188351093145600x^{10}}{(x^{2} + 1)^{13}} + \frac{-125567395430400x^{8}}{(x^{2} + 1)^{12}} + \frac{39953262182400x^{6}}{(x^{2} + 1)^{11}} + \frac{141263319859200x^{10}}{(x^{2} + 1)^{13}} + \frac{11236854988800x^{6}}{(x^{2} + 1)^{11}} + \frac{-2809213747200x^{4}}{(x^{2} + 1)^{10}} + \frac{4815794995200x^{6}}{(x^{2} + 1)^{11}} + \frac{-1203948748800x^{4}}{(x^{2} + 1)^{10}} + \frac{8026324992000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2006581248000x^{4}}{(x^{2} + 1)^{10}} + \frac{-6421059993600x^{4}}{(x^{2} + 1)^{10}} + \frac{267544166400x^{2}}{(x^{2} + 1)^{9}} + \frac{16052649984000x^{6}}{(x^{2} + 1)^{11}} + \frac{-4013162496000x^{4}}{(x^{2} + 1)^{10}} + \frac{13377208320000x^{6}}{(x^{2} + 1)^{11}} + \frac{-3344302080000x^{4}}{(x^{2} + 1)^{10}} + \frac{-10701766656000x^{4}}{(x^{2} + 1)^{10}} + \frac{445906944000x^{2}}{(x^{2} + 1)^{9}} + \frac{5350883328000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2675441664000x^{4}}{(x^{2} + 1)^{10}} + \frac{-2140353331200x^{4}}{(x^{2} + 1)^{10}} + \frac{356725555200x^{2}}{(x^{2} + 1)^{9}} + \frac{-39239811072000x^{8}}{(x^{2} + 1)^{12}} + \frac{12485394432000x^{6}}{(x^{2} + 1)^{11}} + \frac{-24524881920000x^{8}}{(x^{2} + 1)^{12}} + \frac{6688604160000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1672151040000x^{4}}{(x^{2} + 1)^{10}} + \frac{11147673600000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2786918400000x^{4}}{(x^{2} + 1)^{10}} + \frac{-8918138880000x^{4}}{(x^{2} + 1)^{10}} + \frac{371589120000x^{2}}{(x^{2} + 1)^{9}} + \frac{8918138880000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1783627776000x^{4}}{(x^{2} + 1)^{10}} + \frac{297271296000x^{2}}{(x^{2} + 1)^{9}} + \frac{111476736000x^{2}}{(x^{2} + 1)^{9}} + \frac{148635648000x^{2}}{(x^{2} + 1)^{9}} + \frac{-78479622144000x^{8}}{(x^{2} + 1)^{12}} + \frac{21403533312000x^{6}}{(x^{2} + 1)^{11}} + \frac{17836277760000x^{6}}{(x^{2} + 1)^{11}} + \frac{-3567255552000x^{4}}{(x^{2} + 1)^{10}} + \frac{594542592000x^{2}}{(x^{2} + 1)^{9}} + \frac{28538044416000x^{6}}{(x^{2} + 1)^{11}} + \frac{-7134511104000x^{4}}{(x^{2} + 1)^{10}} + \frac{-5707608883200x^{4}}{(x^{2} + 1)^{10}} + \frac{951268147200x^{2}}{(x^{2} + 1)^{9}} + \frac{-8561413324800x^{4}}{(x^{2} + 1)^{10}} + \frac{713451110400x^{2}}{(x^{2} + 1)^{9}} + \frac{237817036800x^{2}}{(x^{2} + 1)^{9}} + \frac{-255058771968000x^{12}}{(x^{2} + 1)^{14}} + \frac{107909480448000x^{10}}{(x^{2} + 1)^{13}} + \frac{98099527680000x^{10}}{(x^{2} + 1)^{13}} + \frac{-36787322880000x^{8}}{(x^{2} + 1)^{12}} + \frac{88289574912000x^{10}}{(x^{2} + 1)^{13}} + \frac{-33108590592000x^{8}}{(x^{2} + 1)^{12}} + \frac{-29429858304000x^{8}}{(x^{2} + 1)^{12}} + \frac{-52319748096000x^{8}}{(x^{2} + 1)^{12}} + \frac{16647192576000x^{6}}{(x^{2} + 1)^{11}} + \frac{-45779779584000x^{8}}{(x^{2} + 1)^{12}} + \frac{14566293504000x^{6}}{(x^{2} + 1)^{11}} + \frac{68669669376000x^{10}}{(x^{2} + 1)^{13}} + \frac{-25751126016000x^{8}}{(x^{2} + 1)^{12}} + \frac{-22889889792000x^{8}}{(x^{2} + 1)^{12}} + \frac{7283146752000x^{6}}{(x^{2} + 1)^{11}} + \frac{-20028653568000x^{8}}{(x^{2} + 1)^{12}} + \frac{6372753408000x^{6}}{(x^{2} + 1)^{11}} + \frac{49049763840000x^{10}}{(x^{2} + 1)^{13}} + \frac{-18393661440000x^{8}}{(x^{2} + 1)^{12}} + \frac{-32699842560000x^{8}}{(x^{2} + 1)^{12}} + \frac{10404495360000x^{6}}{(x^{2} + 1)^{11}} + \frac{-14306181120000x^{8}}{(x^{2} + 1)^{12}} + \frac{4551966720000x^{6}}{(x^{2} + 1)^{11}} + \frac{7803371520000x^{6}}{(x^{2} + 1)^{11}} + \frac{-975421440000x^{4}}{(x^{2} + 1)^{10}} + \frac{-12262440960000x^{8}}{(x^{2} + 1)^{12}} + \frac{3344302080000x^{6}}{(x^{2} + 1)^{11}} + \frac{-836075520000x^{4}}{(x^{2} + 1)^{10}} + \frac{-10218700800000x^{8}}{(x^{2} + 1)^{12}} + \frac{3251404800000x^{6}}{(x^{2} + 1)^{11}} + \frac{2322432000000x^{6}}{(x^{2} + 1)^{11}} + \frac{-580608000000x^{4}}{(x^{2} + 1)^{10}} + \frac{-464486400000x^{4}}{(x^{2} + 1)^{10}} + \frac{77414400000x^{2}}{(x^{2} + 1)^{9}} + \frac{7431782400000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1857945600000x^{4}}{(x^{2} + 1)^{10}} + \frac{-1486356480000x^{4}}{(x^{2} + 1)^{10}} + \frac{247726080000x^{2}}{(x^{2} + 1)^{9}} + \frac{61931520000x^{2}}{(x^{2} + 1)^{9}} + \frac{-8174960640000x^{8}}{(x^{2} + 1)^{12}} + \frac{2601123840000x^{6}}{(x^{2} + 1)^{11}} + \frac{4459069440000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1114767360000x^{4}}{(x^{2} + 1)^{10}} + \frac{11890851840000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2972712960000x^{4}}{(x^{2} + 1)^{10}} + \frac{-4756340736000x^{4}}{(x^{2} + 1)^{10}} + \frac{396361728000x^{2}}{(x^{2} + 1)^{9}} + \frac{99090432000x^{2}}{(x^{2} + 1)^{9}} + \frac{-891813888000x^{4}}{(x^{2} + 1)^{10}} + \frac{-668860416000x^{4}}{(x^{2} + 1)^{10}} + \frac{55738368000x^{2}}{(x^{2} + 1)^{9}} + \frac{37158912000x^{2}}{(x^{2} + 1)^{9}} + \frac{-26159874048000x^{8}}{(x^{2} + 1)^{12}} + \frac{8323596288000x^{6}}{(x^{2} + 1)^{11}} + \frac{4756340736000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1902536294400x^{4}}{(x^{2} + 1)^{10}} + \frac{317089382400x^{2}}{(x^{2} + 1)^{9}} + \frac{79272345600x^{2}}{(x^{2} + 1)^{9}} + \frac{39636172800x^{2}}{(x^{2} + 1)^{9}} + \frac{-204047017574400x^{12}}{(x^{2} + 1)^{14}} + \frac{86327584358400x^{10}}{(x^{2} + 1)^{13}} + \frac{156959244288000x^{10}}{(x^{2} + 1)^{13}} + \frac{-58859716608000x^{8}}{(x^{2} + 1)^{12}} + \frac{54935735500800x^{10}}{(x^{2} + 1)^{13}} + \frac{-41201801625600x^{8}}{(x^{2} + 1)^{12}} + \frac{-36623823667200x^{8}}{(x^{2} + 1)^{12}} + \frac{11653034803200x^{6}}{(x^{2} + 1)^{11}} + \frac{-16022922854400x^{8}}{(x^{2} + 1)^{12}} + \frac{5098202726400x^{6}}{(x^{2} + 1)^{11}} + \frac{17479552204800x^{6}}{(x^{2} + 1)^{11}} + \frac{-27467867750400x^{8}}{(x^{2} + 1)^{12}} + \frac{14982473318400x^{6}}{(x^{2} + 1)^{11}} + \frac{12842119987200x^{6}}{(x^{2} + 1)^{11}} + \frac{10701766656000x^{6}}{(x^{2} + 1)^{11}} + \frac{17122826649600x^{6}}{(x^{2} + 1)^{11}} + \frac{-20927899238400x^{8}}{(x^{2} + 1)^{12}} + \frac{6658877030400x^{6}}{(x^{2} + 1)^{11}} + \frac{11415217766400x^{6}}{(x^{2} + 1)^{11}} + \frac{-2853804441600x^{4}}{(x^{2} + 1)^{10}} + \frac{2378170368000x^{6}}{(x^{2} + 1)^{11}} + \frac{1902536294400x^{6}}{(x^{2} + 1)^{11}} + \frac{-380507258880x^{4}}{(x^{2} + 1)^{10}} + \frac{126835752960x^{2}}{(x^{2} + 1)^{9}} + \frac{-2283043553280x^{4}}{(x^{2} + 1)^{10}} + \frac{380507258880x^{2}}{(x^{2} + 1)^{9}} + \frac{-1712282664960x^{4}}{(x^{2} + 1)^{10}} + \frac{570760888320x^{2}}{(x^{2} + 1)^{9}} + \frac{190253629440x^{2}}{(x^{2} + 1)^{9}} + \frac{-856141332480x^{4}}{(x^{2} + 1)^{10}} + \frac{-1284211998720x^{4}}{(x^{2} + 1)^{10}} + \frac{214035333120x^{2}}{(x^{2} + 1)^{9}} + \frac{-428070666240x^{4}}{(x^{2} + 1)^{10}} + \frac{71345111040x^{2}}{(x^{2} + 1)^{9}} + \frac{3210529996800x^{6}}{(x^{2} + 1)^{11}} + \frac{-321052999680x^{4}}{(x^{2} + 1)^{10}} + \frac{107017666560x^{2}}{(x^{2} + 1)^{9}} + \frac{-240789749760x^{4}}{(x^{2} + 1)^{10}} + \frac{80263249920x^{2}}{(x^{2} + 1)^{9}} + \frac{-15695924428800x^{8}}{(x^{2} + 1)^{12}} + \frac{9988315545600x^{6}}{(x^{2} + 1)^{11}} + \frac{-153035263180800x^{12}}{(x^{2} + 1)^{14}} + \frac{64745688268800x^{10}}{(x^{2} + 1)^{13}} + \frac{58859716608000x^{10}}{(x^{2} + 1)^{13}} + \frac{-22072393728000x^{8}}{(x^{2} + 1)^{12}} + \frac{52973744947200x^{10}}{(x^{2} + 1)^{13}} + \frac{-19865154355200x^{8}}{(x^{2} + 1)^{12}} + \frac{94175546572800x^{10}}{(x^{2} + 1)^{13}} + \frac{-35315829964800x^{8}}{(x^{2} + 1)^{12}} + \frac{41201801625600x^{10}}{(x^{2} + 1)^{13}} + \frac{-15450675609600x^{8}}{(x^{2} + 1)^{12}} + \frac{-13733933875200x^{8}}{(x^{2} + 1)^{12}} + \frac{-12017192140800x^{8}}{(x^{2} + 1)^{12}} + \frac{3823652044800x^{6}}{(x^{2} + 1)^{11}} + \frac{3277416038400x^{6}}{(x^{2} + 1)^{11}} + \frac{-819354009600x^{4}}{(x^{2} + 1)^{10}} + \frac{4682022912000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1170505728000x^{4}}{(x^{2} + 1)^{10}} + \frac{70631659929600x^{10}}{(x^{2} + 1)^{13}} + \frac{-26486872473600x^{8}}{(x^{2} + 1)^{12}} + \frac{-47087773286400x^{8}}{(x^{2} + 1)^{12}} + \frac{-17657914982400x^{8}}{(x^{2} + 1)^{12}} + \frac{5618427494400x^{6}}{(x^{2} + 1)^{11}} + \frac{2407897497600x^{6}}{(x^{2} + 1)^{11}} + \frac{-601974374400x^{4}}{(x^{2} + 1)^{10}} + \frac{133772083200x^{2}}{(x^{2} + 1)^{9}} + \frac{2675441664000x^{6}}{(x^{2} + 1)^{11}} + \frac{44590694400x^{2}}{(x^{2} + 1)^{9}} + \frac{29429858304000x^{10}}{(x^{2} + 1)^{13}} + \frac{-11036196864000x^{8}}{(x^{2} + 1)^{12}} + \frac{-9809952768000x^{8}}{(x^{2} + 1)^{12}} + \frac{6242697216000x^{6}}{(x^{2} + 1)^{11}} + \frac{-8583708672000x^{8}}{(x^{2} + 1)^{12}} + \frac{2731180032000x^{6}}{(x^{2} + 1)^{11}} + \frac{-6131220480000x^{8}}{(x^{2} + 1)^{12}} + \frac{1950842880000x^{6}}{(x^{2} + 1)^{11}} + \frac{1672151040000x^{6}}{(x^{2} + 1)^{11}} + \frac{-418037760000x^{4}}{(x^{2} + 1)^{10}} + \frac{1393459200000x^{6}}{(x^{2} + 1)^{11}} + \frac{-348364800000x^{4}}{(x^{2} + 1)^{10}} + \frac{35315829964800x^{10}}{(x^{2} + 1)^{13}} + \frac{-13243436236800x^{8}}{(x^{2} + 1)^{12}} + \frac{3745618329600x^{6}}{(x^{2} + 1)^{11}} + \frac{1638708019200x^{6}}{(x^{2} + 1)^{11}} + \frac{-351151718400x^{4}}{(x^{2} + 1)^{10}} + \frac{1203948748800x^{6}}{(x^{2} + 1)^{11}} + \frac{-300987187200x^{4}}{(x^{2} + 1)^{10}} + \frac{-7357464576000x^{8}}{(x^{2} + 1)^{12}} + \frac{1170505728000x^{6}}{(x^{2} + 1)^{11}} + \frac{836075520000x^{6}}{(x^{2} + 1)^{11}} + \frac{-209018880000x^{4}}{(x^{2} + 1)^{10}} + \frac{27869184000x^{2}}{(x^{2} + 1)^{9}} + \frac{668860416000x^{6}}{(x^{2} + 1)^{11}} + \frac{-133772083200x^{4}}{(x^{2} + 1)^{10}} + \frac{-401316249600x^{4}}{(x^{2} + 1)^{10}} + \frac{33443020800x^{2}}{(x^{2} + 1)^{9}} + \frac{11147673600x^{2}}{(x^{2} + 1)^{9}} + \frac{-4414478745600x^{8}}{(x^{2} + 1)^{12}} + \frac{702303436800x^{6}}{(x^{2} + 1)^{11}} + \frac{601974374400x^{6}}{(x^{2} + 1)^{11}} + \frac{-150493593600x^{4}}{(x^{2} + 1)^{10}} + \frac{501645312000x^{6}}{(x^{2} + 1)^{11}} + \frac{-125411328000x^{4}}{(x^{2} + 1)^{10}} + \frac{802632499200x^{6}}{(x^{2} + 1)^{11}} + \frac{-160526499840x^{4}}{(x^{2} + 1)^{10}} + \frac{-120394874880x^{4}}{(x^{2} + 1)^{10}} + \frac{26754416640x^{2}}{(x^{2} + 1)^{9}} + \frac{300987187200x^{6}}{(x^{2} + 1)^{11}} + \frac{-75246796800x^{4}}{(x^{2} + 1)^{10}} + \frac{-60197437440x^{4}}{(x^{2} + 1)^{10}} + \frac{-45148078080x^{4}}{(x^{2} + 1)^{10}} + \frac{7524679680x^{2}}{(x^{2} + 1)^{9}} + \frac{-30098718720x^{4}}{(x^{2} + 1)^{10}} + \frac{-11771943321600x^{8}}{(x^{2} + 1)^{12}} + \frac{1872809164800x^{6}}{(x^{2} + 1)^{11}} + \frac{2140353331200x^{6}}{(x^{2} + 1)^{11}} + \frac{-214035333120x^{4}}{(x^{2} + 1)^{10}} + \frac{35672555520x^{2}}{(x^{2} + 1)^{9}} + \frac{-10463949619200x^{8}}{(x^{2} + 1)^{12}} + \frac{3329438515200x^{6}}{(x^{2} + 1)^{11}} + \frac{594542592000x^{6}}{(x^{2} + 1)^{11}} + \frac{-118908518400x^{4}}{(x^{2} + 1)^{10}} + \frac{951268147200x^{6}}{(x^{2} + 1)^{11}} + \frac{-475634073600x^{4}}{(x^{2} + 1)^{10}} + \frac{-190253629440x^{4}}{(x^{2} + 1)^{10}} + \frac{63417876480x^{2}}{(x^{2} + 1)^{9}} + \frac{-71345111040x^{4}}{(x^{2} + 1)^{10}} + \frac{23781703680x^{2}}{(x^{2} + 1)^{9}} + \frac{31708938240x^{2}}{(x^{2} + 1)^{9}} + \frac{-47563407360x^{4}}{(x^{2} + 1)^{10}} + \frac{5284823040x^{2}}{(x^{2} + 1)^{9}} + \frac{-102023508787200x^{12}}{(x^{2} + 1)^{14}} + \frac{43163792179200x^{10}}{(x^{2} + 1)^{13}} + \frac{31391848857600x^{10}}{(x^{2} + 1)^{13}} + \frac{-1248539443200x^{4}}{(x^{2} + 1)^{10}} + \frac{27467867750400x^{10}}{(x^{2} + 1)^{13}} + \frac{-8011461427200x^{8}}{(x^{2} + 1)^{12}} + \frac{2549101363200x^{6}}{(x^{2} + 1)^{11}} + \frac{2184944025600x^{6}}{(x^{2} + 1)^{11}} + \frac{-546236006400x^{4}}{(x^{2} + 1)^{10}} + \frac{-780337152000x^{4}}{(x^{2} + 1)^{10}} + \frac{-13079937024000x^{8}}{(x^{2} + 1)^{12}} + \frac{4161798144000x^{6}}{(x^{2} + 1)^{11}} + \frac{-5722472448000x^{8}}{(x^{2} + 1)^{12}} + \frac{1820786688000x^{6}}{(x^{2} + 1)^{11}} + \frac{-4087480320000x^{8}}{(x^{2} + 1)^{12}} + \frac{1300561920000x^{6}}{(x^{2} + 1)^{11}} + \frac{1114767360000x^{6}}{(x^{2} + 1)^{11}} + \frac{-278691840000x^{4}}{(x^{2} + 1)^{10}} + \frac{928972800000x^{6}}{(x^{2} + 1)^{11}} + \frac{-232243200000x^{4}}{(x^{2} + 1)^{10}} + \frac{-371589120000x^{4}}{(x^{2} + 1)^{10}} + \frac{743178240000x^{6}}{(x^{2} + 1)^{11}} + \frac{49545216000x^{2}}{(x^{2} + 1)^{9}} + \frac{1783627776000x^{6}}{(x^{2} + 1)^{11}} + \frac{1189085184000x^{6}}{(x^{2} + 1)^{11}} + \frac{5885971660800x^{10}}{(x^{2} + 1)^{13}} + \frac{-1961990553600x^{8}}{(x^{2} + 1)^{12}} + \frac{-1716741734400x^{8}}{(x^{2} + 1)^{12}} + \frac{546236006400x^{6}}{(x^{2} + 1)^{11}} + \frac{468202291200x^{6}}{(x^{2} + 1)^{11}} + \frac{-117050572800x^{4}}{(x^{2} + 1)^{10}} + \frac{-1226244096000x^{8}}{(x^{2} + 1)^{12}} + \frac{390168576000x^{6}}{(x^{2} + 1)^{11}} + \frac{334430208000x^{6}}{(x^{2} + 1)^{11}} + \frac{-83607552000x^{4}}{(x^{2} + 1)^{10}} + \frac{278691840000x^{6}}{(x^{2} + 1)^{11}} + \frac{-69672960000x^{4}}{(x^{2} + 1)^{10}} + \frac{-445906944000x^{4}}{(x^{2} + 1)^{10}} + \frac{18579456000x^{2}}{(x^{2} + 1)^{9}} + \frac{-980995276800x^{8}}{(x^{2} + 1)^{12}} + \frac{624269721600x^{6}}{(x^{2} + 1)^{11}} + \frac{445906944000x^{6}}{(x^{2} + 1)^{11}} + \frac{713451110400x^{6}}{(x^{2} + 1)^{11}} + \frac{-178362777600x^{4}}{(x^{2} + 1)^{10}} + \frac{-142690222080x^{4}}{(x^{2} + 1)^{10}} + \frac{47563407360x^{2}}{(x^{2} + 1)^{9}} + \frac{-1471492915200x^{8}}{(x^{2} + 1)^{12}} + \frac{234101145600x^{6}}{(x^{2} + 1)^{11}} + \frac{200658124800x^{6}}{(x^{2} + 1)^{11}} + \frac{-50164531200x^{4}}{(x^{2} + 1)^{10}} + \frac{167215104000x^{6}}{(x^{2} + 1)^{11}} + \frac{-41803776000x^{4}}{(x^{2} + 1)^{10}} + \frac{-66886041600x^{4}}{(x^{2} + 1)^{10}} + \frac{5573836800x^{2}}{(x^{2} + 1)^{9}} + \frac{100329062400x^{6}}{(x^{2} + 1)^{11}} + \frac{-25082265600x^{4}}{(x^{2} + 1)^{10}} + \frac{-40131624960x^{4}}{(x^{2} + 1)^{10}} + \frac{-15049359360x^{4}}{(x^{2} + 1)^{10}} + \frac{2508226560x^{2}}{(x^{2} + 1)^{9}} + \frac{4459069440x^{2}}{(x^{2} + 1)^{9}} + \frac{891813888000x^{6}}{(x^{2} + 1)^{11}} + \frac{1961990553600x^{10}}{(x^{2} + 1)^{13}} + \frac{-1307993702400x^{8}}{(x^{2} + 1)^{12}} + \frac{416179814400x^{6}}{(x^{2} + 1)^{11}} + \frac{-572247244800x^{8}}{(x^{2} + 1)^{12}} + \frac{182078668800x^{6}}{(x^{2} + 1)^{11}} + \frac{-39016857600x^{4}}{(x^{2} + 1)^{10}} + \frac{-490497638400x^{8}}{(x^{2} + 1)^{12}} + \frac{133772083200x^{6}}{(x^{2} + 1)^{11}} + \frac{-44590694400x^{4}}{(x^{2} + 1)^{10}} + \frac{7431782400x^{2}}{(x^{2} + 1)^{9}} + \frac{-408748032000x^{8}}{(x^{2} + 1)^{12}} + \frac{130056192000x^{6}}{(x^{2} + 1)^{11}} + \frac{92897280000x^{6}}{(x^{2} + 1)^{11}} + \frac{-23224320000x^{4}}{(x^{2} + 1)^{10}} + \frac{-18579456000x^{4}}{(x^{2} + 1)^{10}} + \frac{3096576000x^{2}}{(x^{2} + 1)^{9}} + \frac{297271296000x^{6}}{(x^{2} + 1)^{11}} + \frac{-148635648000x^{4}}{(x^{2} + 1)^{10}} + \frac{-59454259200x^{4}}{(x^{2} + 1)^{10}} + \frac{19818086400x^{2}}{(x^{2} + 1)^{9}} + \frac{4954521600x^{2}}{(x^{2} + 1)^{9}} + \frac{-326998425600x^{8}}{(x^{2} + 1)^{12}} + \frac{104044953600x^{6}}{(x^{2} + 1)^{11}} + \frac{-245248819200x^{8}}{(x^{2} + 1)^{12}} + \frac{78033715200x^{6}}{(x^{2} + 1)^{11}} + \frac{66886041600x^{6}}{(x^{2} + 1)^{11}} + \frac{-16721510400x^{4}}{(x^{2} + 1)^{10}} + \frac{55738368000x^{6}}{(x^{2} + 1)^{11}} + \frac{-13934592000x^{4}}{(x^{2} + 1)^{10}} + \frac{33443020800x^{6}}{(x^{2} + 1)^{11}} + \frac{-8360755200x^{4}}{(x^{2} + 1)^{10}} + \frac{-6688604160x^{4}}{(x^{2} + 1)^{10}} + \frac{2229534720x^{2}}{(x^{2} + 1)^{9}} + \frac{-5016453120x^{4}}{(x^{2} + 1)^{10}} + \frac{836075520x^{2}}{(x^{2} + 1)^{9}} + \frac{1114767360x^{2}}{(x^{2} + 1)^{9}} + \frac{-3344302080x^{4}}{(x^{2} + 1)^{10}} + \frac{-17836277760x^{4}}{(x^{2} + 1)^{10}} + \frac{2972712960x^{2}}{(x^{2} + 1)^{9}} + \frac{-163499212800x^{8}}{(x^{2} + 1)^{12}} + \frac{52022476800x^{6}}{(x^{2} + 1)^{11}} + \frac{44590694400x^{6}}{(x^{2} + 1)^{11}} + \frac{-11147673600x^{4}}{(x^{2} + 1)^{10}} + \frac{37158912000x^{6}}{(x^{2} + 1)^{11}} + \frac{-9289728000x^{4}}{(x^{2} + 1)^{10}} + \frac{-14863564800x^{4}}{(x^{2} + 1)^{10}} + \frac{29727129600x^{6}}{(x^{2} + 1)^{11}} + \frac{1321205760x^{2}}{(x^{2} + 1)^{9}} + \frac{-51011754393600x^{12}}{(x^{2} + 1)^{14}} + \frac{21581896089600x^{10}}{(x^{2} + 1)^{13}} + \frac{15695924428800x^{10}}{(x^{2} + 1)^{13}} + \frac{-9155955916800x^{8}}{(x^{2} + 1)^{12}} + \frac{2913258700800x^{6}}{(x^{2} + 1)^{11}} + \frac{13733933875200x^{10}}{(x^{2} + 1)^{13}} + \frac{-4005730713600x^{8}}{(x^{2} + 1)^{12}} + \frac{1274550681600x^{6}}{(x^{2} + 1)^{11}} + \frac{1092472012800x^{6}}{(x^{2} + 1)^{11}} + \frac{-273118003200x^{4}}{(x^{2} + 1)^{10}} + \frac{1560674304000x^{6}}{(x^{2} + 1)^{11}} + \frac{-390168576000x^{4}}{(x^{2} + 1)^{10}} + \frac{-312134860800x^{4}}{(x^{2} + 1)^{10}} + \frac{26011238400x^{2}}{(x^{2} + 1)^{9}} + \frac{11771943321600x^{10}}{(x^{2} + 1)^{13}} + \frac{9809952768000x^{10}}{(x^{2} + 1)^{13}} + \frac{-3269984256000x^{8}}{(x^{2} + 1)^{12}} + \frac{1040449536000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2861236224000x^{8}}{(x^{2} + 1)^{12}} + \frac{910393344000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2043740160000x^{8}}{(x^{2} + 1)^{12}} + \frac{650280960000x^{6}}{(x^{2} + 1)^{11}} + \frac{557383680000x^{6}}{(x^{2} + 1)^{11}} + \frac{-139345920000x^{4}}{(x^{2} + 1)^{10}} + \frac{464486400000x^{6}}{(x^{2} + 1)^{11}} + \frac{-116121600000x^{4}}{(x^{2} + 1)^{10}} + \frac{-185794560000x^{4}}{(x^{2} + 1)^{10}} + \frac{15482880000x^{2}}{(x^{2} + 1)^{9}} + \frac{371589120000x^{6}}{(x^{2} + 1)^{11}} + \frac{7847962214400x^{10}}{(x^{2} + 1)^{13}} + \frac{-2942985830400x^{8}}{(x^{2} + 1)^{12}} + \frac{-2288988979200x^{8}}{(x^{2} + 1)^{12}} + \frac{728314675200x^{6}}{(x^{2} + 1)^{11}} + \frac{-81749606400x^{8}}{(x^{2} + 1)^{12}} + \frac{26011238400x^{6}}{(x^{2} + 1)^{11}} + \frac{22295347200x^{6}}{(x^{2} + 1)^{11}} + \frac{-5573836800x^{4}}{(x^{2} + 1)^{10}} + \frac{18579456000x^{6}}{(x^{2} + 1)^{11}} + \frac{-4644864000x^{4}}{(x^{2} + 1)^{10}} + \frac{-7431782400x^{4}}{(x^{2} + 1)^{10}} + \frac{619315200x^{2}}{(x^{2} + 1)^{9}} + \frac{14863564800x^{6}}{(x^{2} + 1)^{11}} + \frac{-5945425920x^{4}}{(x^{2} + 1)^{10}} + \frac{495452160x^{2}}{(x^{2} + 1)^{9}} + \frac{11147673600x^{6}}{(x^{2} + 1)^{11}} + \frac{-2786918400x^{4}}{(x^{2} + 1)^{10}} + \frac{-1672151040x^{4}}{(x^{2} + 1)^{10}} + \frac{278691840x^{2}}{(x^{2} + 1)^{9}} + \frac{3715891200x^{6}}{(x^{2} + 1)^{11}} + \frac{-928972800x^{4}}{(x^{2} + 1)^{10}} + \frac{-743178240x^{4}}{(x^{2} + 1)^{10}} + \frac{-557383680x^{4}}{(x^{2} + 1)^{10}} + \frac{92897280x^{2}}{(x^{2} + 1)^{9}} + \frac{-371589120x^{4}}{(x^{2} + 1)^{10}} + \frac{82575360x^{2}}{(x^{2} + 1)^{9}} + \frac{660602880x^{2}}{(x^{2} + 1)^{9}} + \frac{-185794560x^{4}}{(x^{2} + 1)^{10}} + \frac{30965760x^{2}}{(x^{2} + 1)^{9}} + \frac{14863564800x^{2}}{(x^{2} + 1)^{9}} + \frac{8918138880x^{2}}{(x^{2} + 1)^{9}} + \frac{165150720x^{2}}{(x^{2} + 1)^{9}} + \frac{10321920x^{2}}{(x^{2} + 1)^{9}} + \frac{-14863564800}{(x^{2} + 1)^{8}} + \frac{-330301440}{(x^{2} + 1)^{8}} + \frac{-3251404800}{(x^{2} + 1)^{8}} + \frac{-8918138880}{(x^{2} + 1)^{8}} + \frac{-5573836800}{(x^{2} + 1)^{8}} + \frac{-4954521600}{(x^{2} + 1)^{8}} + \frac{-743178240}{(x^{2} + 1)^{8}} + \frac{-2322432000}{(x^{2} + 1)^{8}} + \frac{-2477260800}{(x^{2} + 1)^{8}} + \frac{-3963617280}{(x^{2} + 1)^{8}} + \frac{-4644864000}{(x^{2} + 1)^{8}} + \frac{-836075520}{(x^{2} + 1)^{8}} + \frac{-34836480}{(x^{2} + 1)^{8}} + \frac{-15482880}{(x^{2} + 1)^{8}} + \frac{-1238630400}{(x^{2} + 1)^{8}} + \frac{-1672151040}{(x^{2} + 1)^{8}} + \frac{-6193152000}{(x^{2} + 1)^{8}} + \frac{-1393459200}{(x^{2} + 1)^{8}} + \frac{-123863040}{(x^{2} + 1)^{8}} + \frac{-1981808640}{(x^{2} + 1)^{8}} + \frac{-696729600}{(x^{2} + 1)^{8}} + \frac{-11890851840}{(x^{2} + 1)^{8}} + \frac{-313528320}{(x^{2} + 1)^{8}} + \frac{-77414400}{(x^{2} + 1)^{8}} + \frac{-3870720}{(x^{2} + 1)^{8}} + \frac{-990904320}{(x^{2} + 1)^{8}} + \frac{-278691840}{(x^{2} + 1)^{8}} + \frac{-5160960}{(x^{2} + 1)^{8}} + \frac{-1935360000}{(x^{2} + 1)^{8}} + \frac{-41287680}{(x^{2} + 1)^{8}} + \frac{-61931520}{(x^{2} + 1)^{8}} + \frac{-247726080}{(x^{2} + 1)^{8}} + \frac{-1486356480}{(x^{2} + 1)^{8}} + \frac{-154828800}{(x^{2} + 1)^{8}} + \frac{-774144000}{(x^{2} + 1)^{8}} + \frac{-928972800}{(x^{2} + 1)^{8}} + \frac{-69672960}{(x^{2} + 1)^{8}} + \frac{-619315200}{(x^{2} + 1)^{8}} + \frac{-557383680}{(x^{2} + 1)^{8}} + \frac{-82575360}{(x^{2} + 1)^{8}} + \frac{-10321920}{(x^{2} + 1)^{8}} + \frac{-418037760}{(x^{2} + 1)^{8}} + \frac{-645120}{(x^{2} + 1)^{8}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ arccot(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{1428329123020800x^{14}}{(x^{2} + 1)^{15}} + \frac{-663152807116800x^{12}}{(x^{2} + 1)^{14}} + \frac{-612141052723200x^{12}}{(x^{2} + 1)^{14}} + \frac{258982753075200x^{10}}{(x^{2} + 1)^{13}} + \frac{-561129298329600x^{12}}{(x^{2} + 1)^{14}} + \frac{237400856985600x^{10}}{(x^{2} + 1)^{13}} + \frac{431637921792000x^{10}}{(x^{2} + 1)^{13}} + \frac{-80932110336000x^{8}}{(x^{2} + 1)^{12}} + \frac{-510117543936000x^{12}}{(x^{2} + 1)^{14}} + \frac{196199055360000x^{10}}{(x^{2} + 1)^{13}} + \frac{-73574645760000x^{8}}{(x^{2} + 1)^{12}} + \frac{353158299648000x^{10}}{(x^{2} + 1)^{13}} + \frac{-132434362368000x^{8}}{(x^{2} + 1)^{12}} + \frac{-235438866432000x^{8}}{(x^{2} + 1)^{12}} + \frac{74912366592000x^{6}}{(x^{2} + 1)^{11}} + \frac{-459105789542400x^{12}}{(x^{2} + 1)^{14}} + \frac{194237064806400x^{10}}{(x^{2} + 1)^{13}} + \frac{158921234841600x^{10}}{(x^{2} + 1)^{13}} + \frac{-59595463065600x^{8}}{(x^{2} + 1)^{12}} + \frac{-211894979788800x^{8}}{(x^{2} + 1)^{12}} + \frac{16855282483200x^{6}}{(x^{2} + 1)^{11}} + \frac{282526639718400x^{10}}{(x^{2} + 1)^{13}} + \frac{-188351093145600x^{8}}{(x^{2} + 1)^{12}} + \frac{59929893273600x^{6}}{(x^{2} + 1)^{11}} + \frac{-164807206502400x^{8}}{(x^{2} + 1)^{12}} + \frac{52438656614400x^{6}}{(x^{2} + 1)^{11}} + \frac{44947419955200x^{6}}{(x^{2} + 1)^{11}} + \frac{-5618427494400x^{4}}{(x^{2} + 1)^{10}} + \frac{-408094035148800x^{12}}{(x^{2} + 1)^{14}} + \frac{172655168716800x^{10}}{(x^{2} + 1)^{13}} + \frac{313918488576000x^{10}}{(x^{2} + 1)^{13}} + \frac{251134790860800x^{10}}{(x^{2} + 1)^{13}} + \frac{-94175546572800x^{8}}{(x^{2} + 1)^{12}} + \frac{-83711596953600x^{8}}{(x^{2} + 1)^{12}} + \frac{26635508121600x^{6}}{(x^{2} + 1)^{11}} + \frac{-146495294668800x^{8}}{(x^{2} + 1)^{12}} + \frac{46612139212800x^{6}}{(x^{2} + 1)^{11}} + \frac{19976631091200x^{6}}{(x^{2} + 1)^{11}} + \frac{-4994157772800x^{4}}{(x^{2} + 1)^{10}} + \frac{219742942003200x^{10}}{(x^{2} + 1)^{13}} + \frac{-82403603251200x^{8}}{(x^{2} + 1)^{12}} + \frac{-64091691417600x^{8}}{(x^{2} + 1)^{12}} + \frac{20392810905600x^{6}}{(x^{2} + 1)^{11}} + \frac{69918208819200x^{6}}{(x^{2} + 1)^{11}} + \frac{-4369888051200x^{4}}{(x^{2} + 1)^{10}} + \frac{-109871471001600x^{8}}{(x^{2} + 1)^{12}} + \frac{29964946636800x^{6}}{(x^{2} + 1)^{11}} + \frac{-7491236659200x^{4}}{(x^{2} + 1)^{10}} + \frac{49941577728000x^{6}}{(x^{2} + 1)^{11}} + \frac{-6242697216000x^{4}}{(x^{2} + 1)^{10}} + \frac{-2497078886400x^{4}}{(x^{2} + 1)^{10}} + \frac{416179814400x^{2}}{(x^{2} + 1)^{9}} + \frac{-357082280755200x^{12}}{(x^{2} + 1)^{14}} + \frac{151073272627200x^{10}}{(x^{2} + 1)^{13}} + \frac{137339338752000x^{10}}{(x^{2} + 1)^{13}} + \frac{-51502252032000x^{8}}{(x^{2} + 1)^{12}} + \frac{123605404876800x^{10}}{(x^{2} + 1)^{13}} + \frac{-46352026828800x^{8}}{(x^{2} + 1)^{12}} + \frac{96137537126400x^{10}}{(x^{2} + 1)^{13}} + \frac{-36051576422400x^{8}}{(x^{2} + 1)^{12}} + \frac{-32045845708800x^{8}}{(x^{2} + 1)^{12}} + \frac{10196405452800x^{6}}{(x^{2} + 1)^{11}} + \frac{-28040114995200x^{8}}{(x^{2} + 1)^{12}} + \frac{8921854771200x^{6}}{(x^{2} + 1)^{11}} + \frac{30589216358400x^{6}}{(x^{2} + 1)^{11}} + \frac{-1911826022400x^{4}}{(x^{2} + 1)^{10}} + \frac{-24034384281600x^{8}}{(x^{2} + 1)^{12}} + \frac{6554832076800x^{6}}{(x^{2} + 1)^{11}} + \frac{-1638708019200x^{4}}{(x^{2} + 1)^{10}} + \frac{10924720128000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2731180032000x^{4}}{(x^{2} + 1)^{10}} + \frac{-2184944025600x^{4}}{(x^{2} + 1)^{10}} + \frac{182078668800x^{2}}{(x^{2} + 1)^{9}} + \frac{164807206502400x^{10}}{(x^{2} + 1)^{13}} + \frac{-61802702438400x^{8}}{(x^{2} + 1)^{12}} + \frac{-54935735500800x^{8}}{(x^{2} + 1)^{12}} + \frac{-48068768563200x^{8}}{(x^{2} + 1)^{12}} + \frac{13109664153600x^{6}}{(x^{2} + 1)^{11}} + \frac{-3277416038400x^{4}}{(x^{2} + 1)^{10}} + \frac{-2341011456000x^{4}}{(x^{2} + 1)^{10}} + \frac{-3745618329600x^{4}}{(x^{2} + 1)^{10}} + \frac{312134860800x^{2}}{(x^{2} + 1)^{9}} + \frac{-68669669376000x^{8}}{(x^{2} + 1)^{12}} + \frac{21849440256000x^{6}}{(x^{2} + 1)^{11}} + \frac{-4682022912000x^{4}}{(x^{2} + 1)^{10}} + \frac{15606743040000x^{6}}{(x^{2} + 1)^{11}} + \frac{-1950842880000x^{4}}{(x^{2} + 1)^{10}} + \frac{-1560674304000x^{4}}{(x^{2} + 1)^{10}} + \frac{260112384000x^{2}}{(x^{2} + 1)^{9}} + \frac{-936404582400x^{4}}{(x^{2} + 1)^{10}} + \frac{156067430400x^{2}}{(x^{2} + 1)^{9}} + \frac{104044953600x^{2}}{(x^{2} + 1)^{9}} + \frac{-306070526361600x^{12}}{(x^{2} + 1)^{14}} + \frac{129491376537600x^{10}}{(x^{2} + 1)^{13}} + \frac{235438866432000x^{10}}{(x^{2} + 1)^{13}} + \frac{-88289574912000x^{8}}{(x^{2} + 1)^{12}} + \frac{105947489894400x^{10}}{(x^{2} + 1)^{13}} + \frac{-39730308710400x^{8}}{(x^{2} + 1)^{12}} + 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\frac{-980995276800x^{8}}{(x^{2} + 1)^{12}} + \frac{624269721600x^{6}}{(x^{2} + 1)^{11}} + \frac{445906944000x^{6}}{(x^{2} + 1)^{11}} + \frac{713451110400x^{6}}{(x^{2} + 1)^{11}} + \frac{-178362777600x^{4}}{(x^{2} + 1)^{10}} + \frac{-142690222080x^{4}}{(x^{2} + 1)^{10}} + \frac{47563407360x^{2}}{(x^{2} + 1)^{9}} + \frac{-1471492915200x^{8}}{(x^{2} + 1)^{12}} + \frac{234101145600x^{6}}{(x^{2} + 1)^{11}} + \frac{200658124800x^{6}}{(x^{2} + 1)^{11}} + \frac{-50164531200x^{4}}{(x^{2} + 1)^{10}} + \frac{167215104000x^{6}}{(x^{2} + 1)^{11}} + \frac{-41803776000x^{4}}{(x^{2} + 1)^{10}} + \frac{-66886041600x^{4}}{(x^{2} + 1)^{10}} + \frac{5573836800x^{2}}{(x^{2} + 1)^{9}} + \frac{100329062400x^{6}}{(x^{2} + 1)^{11}} + \frac{-25082265600x^{4}}{(x^{2} + 1)^{10}} + \frac{-40131624960x^{4}}{(x^{2} + 1)^{10}} + \frac{-15049359360x^{4}}{(x^{2} + 1)^{10}} + \frac{2508226560x^{2}}{(x^{2} + 1)^{9}} + \frac{4459069440x^{2}}{(x^{2} + 1)^{9}} + \frac{891813888000x^{6}}{(x^{2} + 1)^{11}} + \frac{1961990553600x^{10}}{(x^{2} + 1)^{13}} + \frac{-1307993702400x^{8}}{(x^{2} + 1)^{12}} + \frac{416179814400x^{6}}{(x^{2} + 1)^{11}} + \frac{-572247244800x^{8}}{(x^{2} + 1)^{12}} + \frac{182078668800x^{6}}{(x^{2} + 1)^{11}} + \frac{-39016857600x^{4}}{(x^{2} + 1)^{10}} + \frac{-490497638400x^{8}}{(x^{2} + 1)^{12}} + \frac{133772083200x^{6}}{(x^{2} + 1)^{11}} + \frac{-44590694400x^{4}}{(x^{2} + 1)^{10}} + \frac{7431782400x^{2}}{(x^{2} + 1)^{9}} + \frac{-408748032000x^{8}}{(x^{2} + 1)^{12}} + \frac{130056192000x^{6}}{(x^{2} + 1)^{11}} + \frac{92897280000x^{6}}{(x^{2} + 1)^{11}} + \frac{-23224320000x^{4}}{(x^{2} + 1)^{10}} + \frac{-18579456000x^{4}}{(x^{2} + 1)^{10}} + \frac{3096576000x^{2}}{(x^{2} + 1)^{9}} + \frac{297271296000x^{6}}{(x^{2} + 1)^{11}} + \frac{-148635648000x^{4}}{(x^{2} + 1)^{10}} + \frac{-59454259200x^{4}}{(x^{2} + 1)^{10}} + \frac{19818086400x^{2}}{(x^{2} + 1)^{9}} + \frac{4954521600x^{2}}{(x^{2} + 1)^{9}} + \frac{-326998425600x^{8}}{(x^{2} + 1)^{12}} + \frac{104044953600x^{6}}{(x^{2} + 1)^{11}} + \frac{-245248819200x^{8}}{(x^{2} + 1)^{12}} + \frac{78033715200x^{6}}{(x^{2} + 1)^{11}} + \frac{66886041600x^{6}}{(x^{2} + 1)^{11}} + \frac{-16721510400x^{4}}{(x^{2} + 1)^{10}} + \frac{55738368000x^{6}}{(x^{2} + 1)^{11}} + \frac{-13934592000x^{4}}{(x^{2} + 1)^{10}} + \frac{33443020800x^{6}}{(x^{2} + 1)^{11}} + \frac{-8360755200x^{4}}{(x^{2} + 1)^{10}} + \frac{-6688604160x^{4}}{(x^{2} + 1)^{10}} + \frac{2229534720x^{2}}{(x^{2} + 1)^{9}} + \frac{-5016453120x^{4}}{(x^{2} + 1)^{10}} + \frac{836075520x^{2}}{(x^{2} + 1)^{9}} + \frac{1114767360x^{2}}{(x^{2} + 1)^{9}} + \frac{-3344302080x^{4}}{(x^{2} + 1)^{10}} + \frac{-17836277760x^{4}}{(x^{2} + 1)^{10}} + \frac{2972712960x^{2}}{(x^{2} + 1)^{9}} + \frac{-163499212800x^{8}}{(x^{2} + 1)^{12}} + \frac{52022476800x^{6}}{(x^{2} + 1)^{11}} + \frac{44590694400x^{6}}{(x^{2} + 1)^{11}} + \frac{-11147673600x^{4}}{(x^{2} + 1)^{10}} + \frac{37158912000x^{6}}{(x^{2} + 1)^{11}} + \frac{-9289728000x^{4}}{(x^{2} + 1)^{10}} + \frac{-14863564800x^{4}}{(x^{2} + 1)^{10}} + \frac{29727129600x^{6}}{(x^{2} + 1)^{11}} + \frac{1321205760x^{2}}{(x^{2} + 1)^{9}} + \frac{-51011754393600x^{12}}{(x^{2} + 1)^{14}} + \frac{21581896089600x^{10}}{(x^{2} + 1)^{13}} + \frac{15695924428800x^{10}}{(x^{2} + 1)^{13}} + \frac{-9155955916800x^{8}}{(x^{2} + 1)^{12}} + \frac{2913258700800x^{6}}{(x^{2} + 1)^{11}} + \frac{13733933875200x^{10}}{(x^{2} + 1)^{13}} + \frac{-4005730713600x^{8}}{(x^{2} + 1)^{12}} + \frac{1274550681600x^{6}}{(x^{2} + 1)^{11}} + \frac{1092472012800x^{6}}{(x^{2} + 1)^{11}} + \frac{-273118003200x^{4}}{(x^{2} + 1)^{10}} + \frac{1560674304000x^{6}}{(x^{2} + 1)^{11}} + \frac{-390168576000x^{4}}{(x^{2} + 1)^{10}} + \frac{-312134860800x^{4}}{(x^{2} + 1)^{10}} + \frac{26011238400x^{2}}{(x^{2} + 1)^{9}} + \frac{11771943321600x^{10}}{(x^{2} + 1)^{13}} + \frac{9809952768000x^{10}}{(x^{2} + 1)^{13}} + \frac{-3269984256000x^{8}}{(x^{2} + 1)^{12}} + \frac{1040449536000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2861236224000x^{8}}{(x^{2} + 1)^{12}} + \frac{910393344000x^{6}}{(x^{2} + 1)^{11}} + \frac{-2043740160000x^{8}}{(x^{2} + 1)^{12}} + \frac{650280960000x^{6}}{(x^{2} + 1)^{11}} + \frac{557383680000x^{6}}{(x^{2} + 1)^{11}} + \frac{-139345920000x^{4}}{(x^{2} + 1)^{10}} + \frac{464486400000x^{6}}{(x^{2} + 1)^{11}} + \frac{-116121600000x^{4}}{(x^{2} + 1)^{10}} + \frac{-185794560000x^{4}}{(x^{2} + 1)^{10}} + \frac{15482880000x^{2}}{(x^{2} + 1)^{9}} + \frac{371589120000x^{6}}{(x^{2} + 1)^{11}} + \frac{7847962214400x^{10}}{(x^{2} + 1)^{13}} + \frac{-2942985830400x^{8}}{(x^{2} + 1)^{12}} + \frac{-2288988979200x^{8}}{(x^{2} + 1)^{12}} + \frac{728314675200x^{6}}{(x^{2} + 1)^{11}} + \frac{-81749606400x^{8}}{(x^{2} + 1)^{12}} + \frac{26011238400x^{6}}{(x^{2} + 1)^{11}} + \frac{22295347200x^{6}}{(x^{2} + 1)^{11}} + \frac{-5573836800x^{4}}{(x^{2} + 1)^{10}} + \frac{18579456000x^{6}}{(x^{2} + 1)^{11}} + \frac{-4644864000x^{4}}{(x^{2} + 1)^{10}} + \frac{-7431782400x^{4}}{(x^{2} + 1)^{10}} + \frac{619315200x^{2}}{(x^{2} + 1)^{9}} + \frac{14863564800x^{6}}{(x^{2} + 1)^{11}} + \frac{-5945425920x^{4}}{(x^{2} + 1)^{10}} + \frac{495452160x^{2}}{(x^{2} + 1)^{9}} + \frac{11147673600x^{6}}{(x^{2} + 1)^{11}} + \frac{-2786918400x^{4}}{(x^{2} + 1)^{10}} + \frac{-1672151040x^{4}}{(x^{2} + 1)^{10}} + \frac{278691840x^{2}}{(x^{2} + 1)^{9}} + \frac{3715891200x^{6}}{(x^{2} + 1)^{11}} + \frac{-928972800x^{4}}{(x^{2} + 1)^{10}} + \frac{-743178240x^{4}}{(x^{2} + 1)^{10}} + \frac{-557383680x^{4}}{(x^{2} + 1)^{10}} + \frac{92897280x^{2}}{(x^{2} + 1)^{9}} + \frac{-371589120x^{4}}{(x^{2} + 1)^{10}} + \frac{82575360x^{2}}{(x^{2} + 1)^{9}} + \frac{660602880x^{2}}{(x^{2} + 1)^{9}} + \frac{-185794560x^{4}}{(x^{2} + 1)^{10}} + \frac{30965760x^{2}}{(x^{2} + 1)^{9}} + \frac{14863564800x^{2}}{(x^{2} + 1)^{9}} + \frac{8918138880x^{2}}{(x^{2} + 1)^{9}} + \frac{165150720x^{2}}{(x^{2} + 1)^{9}} + \frac{10321920x^{2}}{(x^{2} + 1)^{9}} + \frac{-14863564800}{(x^{2} + 1)^{8}} + \frac{-330301440}{(x^{2} + 1)^{8}} + \frac{-3251404800}{(x^{2} + 1)^{8}} + \frac{-8918138880}{(x^{2} + 1)^{8}} + \frac{-5573836800}{(x^{2} + 1)^{8}} + \frac{-4954521600}{(x^{2} + 1)^{8}} + \frac{-743178240}{(x^{2} + 1)^{8}} + \frac{-2322432000}{(x^{2} + 1)^{8}} + \frac{-2477260800}{(x^{2} + 1)^{8}} + \frac{-3963617280}{(x^{2} + 1)^{8}} + \frac{-4644864000}{(x^{2} + 1)^{8}} + \frac{-836075520}{(x^{2} + 1)^{8}} + \frac{-34836480}{(x^{2} + 1)^{8}} + \frac{-15482880}{(x^{2} + 1)^{8}} + \frac{-1238630400}{(x^{2} + 1)^{8}} + \frac{-1672151040}{(x^{2} + 1)^{8}} + \frac{-6193152000}{(x^{2} + 1)^{8}} + \frac{-1393459200}{(x^{2} + 1)^{8}} + \frac{-123863040}{(x^{2} + 1)^{8}} + \frac{-1981808640}{(x^{2} + 1)^{8}} + \frac{-696729600}{(x^{2} + 1)^{8}} + \frac{-11890851840}{(x^{2} + 1)^{8}} + \frac{-313528320}{(x^{2} + 1)^{8}} + \frac{-77414400}{(x^{2} + 1)^{8}} + \frac{-3870720}{(x^{2} + 1)^{8}} + \frac{-990904320}{(x^{2} + 1)^{8}} + \frac{-278691840}{(x^{2} + 1)^{8}} + \frac{-5160960}{(x^{2} + 1)^{8}} + \frac{-1935360000}{(x^{2} + 1)^{8}} + \frac{-41287680}{(x^{2} + 1)^{8}} + \frac{-61931520}{(x^{2} + 1)^{8}} + \frac{-247726080}{(x^{2} + 1)^{8}} + \frac{-1486356480}{(x^{2} + 1)^{8}} + \frac{-154828800}{(x^{2} + 1)^{8}} + \frac{-774144000}{(x^{2} + 1)^{8}} + \frac{-928972800}{(x^{2} + 1)^{8}} + \frac{-69672960}{(x^{2} + 1)^{8}} + \frac{-619315200}{(x^{2} + 1)^{8}} + \frac{-557383680}{(x^{2} + 1)^{8}} + \frac{-82575360}{(x^{2} + 1)^{8}} + \frac{-10321920}{(x^{2} + 1)^{8}} + \frac{-418037760}{(x^{2} + 1)^{8}} + \frac{-645120}{(x^{2} + 1)^{8}}\\ \end{split}\end{equation} \]