数学
         
语言:中文    Language:English
求导函数:
    输入一个原函数(即需要求导的函数),然后设置需要求导的变量和求导的阶数,点击“下一步”按钮,即可获得该函数相应阶数的导函数。
    注意,输入的函数支持数学函数和其它常量。
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    本次共计算 1 个题目:每一题对 x 求 15 阶导数。
    注意,变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{{x}^{7}}{sin(x)} + 15x - cos(e^{x} - ln(x) + 3) - tan(x) 关于 x 的 15 阶导数:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{7}}{sin(x)} + 15x - cos(e^{x} - ln(x) + 3) - tan(x)\\\\ &\color{blue}{函数的 15 阶导数:} \\=&\frac{1307674368000cos^{8}(x)}{sin^{9}(x)} + \frac{3269185920000cos^{6}(x)}{sin^{7}(x)} + \frac{2713424313600cos^{4}(x)}{sin^{5}(x)} + \frac{796799203200cos^{2}(x)}{sin^{3}(x)} + \frac{44918874000}{sin(x)} - \frac{9153720576000xcos^{9}(x)}{sin^{10}(x)} - \frac{25935541632000xcos^{7}(x)}{sin^{8}(x)} - \frac{25808406624000xcos^{5}(x)}{sin^{6}(x)} - \frac{10300962672000xcos^{3}(x)}{sin^{4}(x)} - \frac{1274402329200xcos(x)}{sin^{2}(x)} + \frac{10035507802320x^{2}cos^{2}(x)}{sin^{3}(x)} + \frac{51073765142400x^{2}cos^{4}(x)}{sin^{5}(x)} + \frac{100919769350400x^{2}cos^{6}(x)}{sin^{7}(x)} + \frac{86960345472000x^{2}cos^{8}(x)}{sin^{9}(x)} + \frac{27461161728000x^{2}cos^{10}(x)}{sin^{11}(x)} - \frac{3098990349000x^{3}cos(x)}{sin^{2}(x)} - \frac{35515391511600x^{3}cos^{3}(x)}{sin^{4}(x)} + \frac{9395346269400x^{4}cos^{2}(x)}{sin^{3}(x)} - \frac{130437491184000x^{3}cos^{5}(x)}{sin^{6}(x)} + \frac{66187418497200x^{4}cos^{4}(x)}{sin^{5}(x)} - \frac{212442598368000x^{3}cos^{7}(x)}{sin^{8}(x)} + \frac{189143594640000x^{4}cos^{6}(x)}{sin^{7}(x)} - \frac{879181926210x^{5}cos(x)}{sin^{2}(x)} - \frac{160190110080000x^{3}cos^{9}(x)}{sin^{10}(x)} - \frac{13520109821400x^{5}cos^{3}(x)}{sin^{4}(x)} + \frac{1007587936110x^{6}cos^{2}(x)}{sin^{3}(x)} + \frac{261770981472000x^{4}cos^{8}(x)}{sin^{9}(x)} - \frac{67652245861200x^{5}cos^{5}(x)}{sin^{6}(x)} + \frac{9341468299800x^{6}cos^{4}(x)}{sin^{5}(x)} - \frac{19391512145x^{7}cos(x)}{sin^{2}(x)} - \frac{45768602880000x^{3}cos^{11}(x)}{sin^{12}(x)} - \frac{157761831427200x^{5}cos^{7}(x)}{sin^{8}(x)} - \frac{384653685786x^{7}cos^{3}(x)}{sin^{4}(x)} + \frac{35958245122800x^{6}cos^{6}(x)}{sin^{7}(x)} - \frac{2499588687960x^{7}cos^{5}(x)}{sin^{6}(x)} + \frac{175446311040000x^{4}cos^{10}(x)}{sin^{11}(x)} - \frac{189710858937600x^{5}cos^{9}(x)}{sin^{10}(x)} - \frac{7784050594320x^{7}cos^{7}(x)}{sin^{8}(x)} + \frac{70702199568000x^{6}cos^{8}(x)}{sin^{9}(x)} + \frac{45768602880000x^{4}cos^{12}(x)}{sin^{13}(x)} - \frac{13216073270400x^{7}cos^{9}(x)}{sin^{10}(x)} + \frac{75136789728000x^{6}cos^{10}(x)}{sin^{11}(x)} - \frac{12579100934400x^{7}cos^{11}(x)}{sin^{12}(x)} - \frac{114421507200000x^{5}cos^{11}(x)}{sin^{12}(x)} + \frac{41191742592000x^{6}cos^{12}(x)}{sin^{13}(x)} - \frac{6320426112000x^{7}cos^{13}(x)}{sin^{14}(x)} - \frac{27461161728000x^{5}cos^{13}(x)}{sin^{14}(x)} + \frac{9153720576000x^{6}cos^{14}(x)}{sin^{15}(x)} - \frac{1307674368000x^{7}cos^{15}(x)}{sin^{16}(x)} + \frac{20932903005x^{6}}{sin(x)} + \frac{258249195750x^{4}}{sin(x)} + \frac{382320698760x^{2}}{sin(x)} + e^{x}sin(e^{x} - ln(x) + 3) + 16383e^{{x}*{2}}cos(e^{x} - ln(x) + 3) - \frac{15e^{x}cos(e^{x} - ln(x) + 3)}{x} - 2375101e^{{x}*{3}}sin(e^{x} - ln(x) + 3) + \frac{122865e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x} + \frac{105e^{x}cos(e^{x} - ln(x) + 3)}{x^{2}} - \frac{105e^{x}sin(e^{x} - ln(x) + 3)}{x^{2}} - 42355950e^{{x}*{4}}cos(e^{x} - ln(x) + 3) + \frac{11834550e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x} - \frac{429975e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{2}} - \frac{429975e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{2}} - \frac{455e^{x}cos(e^{x} - ln(x) + 3)}{x^{3}} + \frac{1365e^{x}sin(e^{x} - ln(x) + 3)}{x^{3}} + 210766920e^{{x}*{5}}sin(e^{x} - ln(x) + 3) - \frac{155876175e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x} - \frac{27470625e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{2}} + \frac{27470625e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{2}} + \frac{931385e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{3}} + \frac{2794155e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{3}} - \frac{13650e^{x}sin(e^{x} - ln(x) + 3)}{x^{4}} + 420693273e^{{x}*{6}}cos(e^{x} - ln(x) + 3) - \frac{601125525e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x} + \frac{265915650e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{2}} + \frac{265915650e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{2}} + \frac{39369330e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{3}} - \frac{118107990e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{3}} - \frac{13963950e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{4}} + \frac{120120e^{x}sin(e^{x} - ln(x) + 3)}{x^{5}} + \frac{30030e^{x}cos(e^{x} - ln(x) + 3)}{x^{5}} - 408741333e^{{x}*{7}}sin(e^{x} - ln(x) + 3) + \frac{951545595e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x} + \frac{788392605e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{2}} - \frac{788392605e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{2}} - \frac{278232955e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{3}} - \frac{834698865e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{3}} + \frac{389038650e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{4}} + \frac{61381320e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{5}} - \frac{15345330e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{5}} - \frac{950950e^{x}sin(e^{x} - ln(x) + 3)}{x^{6}} - \frac{450450e^{x}cos(e^{x} - ln(x) + 3)}{x^{6}} - 216627840e^{{x}*{8}}cos(e^{x} - ln(x) + 3) + \frac{739939200e^{{x}*{7}}cos(e^{x} - ln(x) + 3)}{x} - \frac{978737760e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x^{2}} - \frac{978737760e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{2}} - \frac{627627000e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{3}} + \frac{1882881000e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{3}} + \frac{1989487500e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{4}} - \frac{1120719600e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{5}} - \frac{280179900e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{5}} - \frac{242492250e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{6}} + \frac{114864750e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{6}} + \frac{6756750e^{x}sin(e^{x} - ln(x) + 3)}{x^{7}} + \frac{4697550e^{x}cos(e^{x} - ln(x) + 3)}{x^{7}} + 67128490e^{{x}*{9}}sin(e^{x} - ln(x) + 3) - \frac{313684800e^{{x}*{8}}sin(e^{x} - ln(x) + 3)}{x} - \frac{600119520e^{{x}*{7}}cos(e^{x} - ln(x) + 3)}{x^{2}} + \frac{600119520e^{{x}*{7}}sin(e^{x} - ln(x) + 3)}{x^{2}} + \frac{602261660e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x^{3}} + \frac{1806784980e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{3}} - \frac{3367864500e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{4}} - \frac{4096692600e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{5}} + \frac{1024173150e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{5}} + \frac{2876623750e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{6}} + \frac{1362611250e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{6}} + \frac{858107250e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{7}} - \frac{596588850e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{7}} - \frac{42599700e^{x}sin(e^{x} - ln(x) + 3)}{x^{8}} - \frac{39639600e^{x}cos(e^{x} - ln(x) + 3)}{x^{8}} + 12662650e^{{x}*{10}}cos(e^{x} - ln(x) + 3) - \frac{77026950e^{{x}*{9}}cos(e^{x} - ln(x) + 3)}{x} + \frac{199459260e^{{x}*{8}}sin(e^{x} - ln(x) + 3)}{x^{2}} + \frac{199459260e^{{x}*{8}}cos(e^{x} - ln(x) + 3)}{x^{2}} + \frac{285465180e^{{x}*{7}}cos(e^{x} - ln(x) + 3)}{x^{3}} - \frac{856395540e^{{x}*{7}}sin(e^{x} - ln(x) + 3)}{x^{3}} - \frac{2449997550e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{4}} + \frac{5108103000e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{5}} + \frac{1277025750e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{5}} + \frac{7388881500e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{6}} - \frac{3499996500e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{6}} - \frac{6527020500e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{7}} - \frac{4537833300e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{7}} - \frac{2683781100e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{8}} + \frac{2497294800e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{8}} + \frac{234234000e^{x}sin(e^{x} - ln(x) + 3)}{x^{9}} + \frac{279779500e^{x}cos(e^{x} - ln(x) + 3)}{x^{9}} - 1479478e^{{x}*{11}}sin(e^{x} - ln(x) + 3) + \frac{11291280e^{{x}*{10}}sin(e^{x} - ln(x) + 3)}{x} + \frac{37747710e^{{x}*{9}}cos(e^{x} - ln(x) + 3)}{x^{2}} - \frac{37747710e^{{x}*{9}}sin(e^{x} - ln(x) + 3)}{x^{2}} - \frac{72357285e^{{x}*{8}}sin(e^{x} - ln(x) + 3)}{x^{3}} - \frac{217071855e^{{x}*{8}}cos(e^{x} - ln(x) + 3)}{x^{3}} + \frac{873422550e^{{x}*{7}}sin(e^{x} - ln(x) + 3)}{x^{4}} + \frac{2741979240e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{5}} - \frac{685494810e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x^{5}} - \frac{6610053450e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{6}} - \frac{3131077950e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{6}} - \frac{11493231750e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{7}} + \frac{7990532550e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{7}} + \frac{12822509700e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{8}} + \frac{11931519600e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{8}} + \frac{7261254000e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{9}} - \frac{8673164500e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{9}} - \frac{1096995900e^{x}sin(e^{x} - ln(x) + 3)}{x^{10}} - \frac{1651349700e^{x}cos(e^{x} - ln(x) + 3)}{x^{10}} - 106470e^{{x}*{12}}cos(e^{x} - ln(x) + 3) + \frac{990990e^{{x}*{11}}cos(e^{x} - ln(x) + 3)}{x} - \frac{4129125e^{{x}*{10}}sin(e^{x} - ln(x) + 3)}{x^{2}} - \frac{4129125e^{{x}*{10}}cos(e^{x} - ln(x) + 3)}{x^{2}} - \frac{10135125e^{{x}*{9}}cos(e^{x} - ln(x) + 3)}{x^{3}} + \frac{30405375e^{{x}*{9}}sin(e^{x} - ln(x) + 3)}{x^{3}} + \frac{162162000e^{{x}*{8}}cos(e^{x} - ln(x) + 3)}{x^{4}} - \frac{706305600e^{{x}*{7}}sin(e^{x} - ln(x) + 3)}{x^{5}} - \frac{176576400e^{{x}*{7}}cos(e^{x} - ln(x) + 3)}{x^{5}} - \frac{2516213700e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{6}} + \frac{1191890700e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x^{6}} + \frac{7094587500e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{7}} + \frac{4932427500e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{7}} + \frac{14909895000e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{8}} - \frac{13873860000e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{8}} - \frac{21081060000e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{9}} - \frac{25180155000e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{9}} - \frac{16454938500e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{10}} + \frac{24770245500e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{10}} + \frac{4235731500e^{x}sin(e^{x} - ln(x) + 3)}{x^{11}} + \frac{8004769500e^{x}cos(e^{x} - ln(x) + 3)}{x^{11}} + 4550e^{{x}*{13}}sin(e^{x} - ln(x) + 3) - \frac{50505e^{{x}*{12}}sin(e^{x} - ln(x) + 3)}{x} - \frac{255255e^{{x}*{11}}cos(e^{x} - ln(x) + 3)}{x^{2}} + \frac{255255e^{{x}*{11}}sin(e^{x} - ln(x) + 3)}{x^{2}} + \frac{775775e^{{x}*{10}}sin(e^{x} - ln(x) + 3)}{x^{3}} + \frac{2327325e^{{x}*{10}}cos(e^{x} - ln(x) + 3)}{x^{3}} - \frac{15765750e^{{x}*{9}}sin(e^{x} - ln(x) + 3)}{x^{4}} - \frac{90090000e^{{x}*{8}}cos(e^{x} - ln(x) + 3)}{x^{5}} + \frac{22522500e^{{x}*{8}}sin(e^{x} - ln(x) + 3)}{x^{5}} + \frac{439338900e^{{x}*{7}}sin(e^{x} - ln(x) + 3)}{x^{6}} + \frac{208107900e^{{x}*{7}}cos(e^{x} - ln(x) + 3)}{x^{6}} + \frac{1797295500e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{7}} - \frac{1249548300e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x^{7}} - \frac{5963958000e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{8}} - \frac{5549544000e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{8}} - \frac{15225210000e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{9}} + \frac{18185667500e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{9}} + \frac{27424897500e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{10}} + \frac{41283742500e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{10}} + \frac{29650120500e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{11}} - \frac{56033386500e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{11}} - \frac{12862759000e^{x}sin(e^{x} - ln(x) + 3)}{x^{12}} - \frac{30762732000e^{x}cos(e^{x} - ln(x) + 3)}{x^{12}} + 105e^{{x}*{14}}cos(e^{x} - ln(x) + 3) - \frac{1365e^{{x}*{13}}cos(e^{x} - ln(x) + 3)}{x} + \frac{8190e^{{x}*{12}}sin(e^{x} - ln(x) + 3)}{x^{2}} + \frac{8190e^{{x}*{12}}cos(e^{x} - ln(x) + 3)}{x^{2}} + \frac{30030e^{{x}*{11}}cos(e^{x} - ln(x) + 3)}{x^{3}} - \frac{90090e^{{x}*{11}}sin(e^{x} - ln(x) + 3)}{x^{3}} - \frac{750750e^{{x}*{10}}cos(e^{x} - ln(x) + 3)}{x^{4}} + \frac{5405400e^{{x}*{9}}sin(e^{x} - ln(x) + 3)}{x^{5}} + \frac{1351350e^{{x}*{9}}cos(e^{x} - ln(x) + 3)}{x^{5}} + \frac{34234200e^{{x}*{8}}cos(e^{x} - ln(x) + 3)}{x^{6}} - \frac{16216200e^{{x}*{8}}sin(e^{x} - ln(x) + 3)}{x^{6}} - \frac{189189000e^{{x}*{7}}sin(e^{x} - ln(x) + 3)}{x^{7}} - \frac{131531400e^{{x}*{7}}cos(e^{x} - ln(x) + 3)}{x^{7}} - \frac{894593700e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{8}} + \frac{832431600e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x^{8}} + \frac{3513510000e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{9}} + \frac{4196692500e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{9}} + \frac{10969959000e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{10}} - \frac{16513497000e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{10}} - \frac{25414389000e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{11}} - \frac{48028617000e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{11}} - \frac{38588277000e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{12}} + \frac{92288196000e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{12}} + \frac{28520856000e^{x}sin(e^{x} - ln(x) + 3)}{x^{13}} + \frac{88157433000e^{x}cos(e^{x} - ln(x) + 3)}{x^{13}} - e^{{x}*{15}}sin(e^{x} - ln(x) + 3) + \frac{15e^{{x}*{14}}sin(e^{x} - ln(x) + 3)}{x} + \frac{105e^{{x}*{13}}cos(e^{x} - ln(x) + 3)}{x^{2}} - \frac{105e^{{x}*{13}}sin(e^{x} - ln(x) + 3)}{x^{2}} - \frac{455e^{{x}*{12}}sin(e^{x} - ln(x) + 3)}{x^{3}} - \frac{1365e^{{x}*{12}}cos(e^{x} - ln(x) + 3)}{x^{3}} + \frac{13650e^{{x}*{11}}sin(e^{x} - ln(x) + 3)}{x^{4}} + \frac{120120e^{{x}*{10}}cos(e^{x} - ln(x) + 3)}{x^{5}} - \frac{30030e^{{x}*{10}}sin(e^{x} - ln(x) + 3)}{x^{5}} - \frac{950950e^{{x}*{9}}sin(e^{x} - ln(x) + 3)}{x^{6}} - \frac{450450e^{{x}*{9}}cos(e^{x} - ln(x) + 3)}{x^{6}} - \frac{6756750e^{{x}*{8}}cos(e^{x} - ln(x) + 3)}{x^{7}} + \frac{4697550e^{{x}*{8}}sin(e^{x} - ln(x) + 3)}{x^{7}} + \frac{42599700e^{{x}*{7}}sin(e^{x} - ln(x) + 3)}{x^{8}} + \frac{39639600e^{{x}*{7}}cos(e^{x} - ln(x) + 3)}{x^{8}} + \frac{234234000e^{{x}*{6}}cos(e^{x} - ln(x) + 3)}{x^{9}} - \frac{279779500e^{{x}*{6}}sin(e^{x} - ln(x) + 3)}{x^{9}} - \frac{1096995900e^{{x}*{5}}sin(e^{x} - ln(x) + 3)}{x^{10}} - \frac{1651349700e^{{x}*{5}}cos(e^{x} - ln(x) + 3)}{x^{10}} - \frac{4235731500e^{{x}*{4}}cos(e^{x} - ln(x) + 3)}{x^{11}} + \frac{8004769500e^{{x}*{4}}sin(e^{x} - ln(x) + 3)}{x^{11}} + \frac{12862759000e^{{x}*{3}}sin(e^{x} - ln(x) + 3)}{x^{12}} + \frac{30762732000e^{{x}*{3}}cos(e^{x} - ln(x) + 3)}{x^{12}} + \frac{28520856000e^{{x}*{2}}cos(e^{x} - ln(x) + 3)}{x^{13}} - \frac{88157433000e^{{x}*{2}}sin(e^{x} - ln(x) + 3)}{x^{13}} - \frac{40373385000e^{x}sin(e^{x} - ln(x) + 3)}{x^{14}} - \frac{167795355000e^{x}cos(e^{x} - ln(x) + 3)}{x^{14}} - \frac{26495469000cos(e^{x} - ln(x) + 3)}{x^{15}} + \frac{159300557000sin(e^{x} - ln(x) + 3)}{x^{15}} - 1903757312sec^{16}(x) - 89702612992tan^{2}(x)sec^{14}(x) - 460858269696tan^{4}(x)sec^{12}(x) - 559148810240tan^{6}(x)sec^{10}(x) - 182172651520tan^{8}(x)sec^{8}(x) - 13754155008tan^{10}(x)sec^{6}(x) - 134094848tan^{12}(x)sec^{4}(x) - 16384tan^{14}(x)sec^{2}(x)\\ \end{split}\end{equation} \]



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