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。
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。
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。
\[ \begin{equation}\begin{split}【1/1】求函数xsqrt(sin(e^{x})) 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 15 阶导数：} \\=&\frac{15e^{x}cos(e^{x})}{2sin^{\frac{1}{2}}(e^{x})} - \frac{122865e^{{x}*{2}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{5917275e^{{x}*{3}}cos(e^{x})}{2sin^{\frac{1}{2}}(e^{x})} + \frac{17751825e^{{x}*{3}}cos^{3}(e^{x})}{4sin^{\frac{5}{2}}(e^{x})} - \frac{779380875e^{{x}*{4}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{11421384975e^{{x}*{5}}cos(e^{x})}{8sin^{\frac{1}{2}}(e^{x})} - \frac{2338142625e^{{x}*{4}}cos^{4}(e^{x})}{16sin^{\frac{7}{2}}(e^{x})} + \frac{27050648625e^{{x}*{5}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{274996676955e^{{x}*{6}}cos^{2}(e^{x})}{16sin^{\frac{3}{2}}(e^{x})} + \frac{25851625800e^{{x}*{7}}cos(e^{x})}{sin^{\frac{1}{2}}(e^{x})} + \frac{63118180125e^{{x}*{5}}cos^{5}(e^{x})}{32sin^{\frac{9}{2}}(e^{x})} - \frac{927756955125e^{{x}*{6}}cos^{4}(e^{x})}{32sin^{\frac{7}{2}}(e^{x})} + \frac{110227817700e^{{x}*{7}}cos^{3}(e^{x})}{sin^{\frac{5}{2}}(e^{x})} - \frac{145667379000e^{{x}*{8}}cos^{2}(e^{x})}{sin^{\frac{3}{2}}(e^{x})} + \frac{1123091444475e^{{x}*{9}}cos(e^{x})}{16sin^{\frac{1}{2}}(e^{x})} - \frac{899210587275e^{{x}*{6}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{144461567250e^{{x}*{7}}cos^{5}(e^{x})}{sin^{\frac{9}{2}}(e^{x})} - \frac{423033360750e^{{x}*{8}}cos^{4}(e^{x})}{sin^{\frac{7}{2}}(e^{x})} + \frac{3753330706125e^{{x}*{9}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{845872832805e^{{x}*{10}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{1173372295095e^{{x}*{11}}cos(e^{x})}{32sin^{\frac{1}{2}}(e^{x})} + \frac{60091156125e^{{x}*{7}}cos^{7}(e^{x})}{sin^{\frac{13}{2}}(e^{x})} - \frac{453911708250e^{{x}*{8}}cos^{6}(e^{x})}{sin^{\frac{11}{2}}(e^{x})} + \frac{33034740613875e^{{x}*{9}}cos^{5}(e^{x})}{32sin^{\frac{9}{2}}(e^{x})} - \frac{3714319483875e^{{x}*{10}}cos^{4}(e^{x})}{4sin^{\frac{7}{2}}(e^{x})} + \frac{22645143706185e^{{x}*{11}}cos^{3}(e^{x})}{64sin^{\frac{5}{2}}(e^{x})} - \frac{3522074003175e^{{x}*{12}}cos^{2}(e^{x})}{64sin^{\frac{3}{2}}(e^{x})} + \frac{377532326535e^{{x}*{13}}cos(e^{x})}{128sin^{\frac{1}{2}}(e^{x})} - \frac{662340553875e^{{x}*{8}}cos^{8}(e^{x})}{4sin^{\frac{15}{2}}(e^{x})} + \frac{30026067946875e^{{x}*{9}}cos^{7}(e^{x})}{32sin^{\frac{13}{2}}(e^{x})} - \frac{331678969035e^{{x}*{14}}cos^{2}(e^{x})}{256sin^{\frac{3}{2}}(e^{x})} - \frac{13150428065775e^{{x}*{10}}cos^{6}(e^{x})}{8sin^{\frac{11}{2}}(e^{x})} + \frac{4967542309275e^{{x}*{13}}cos^{3}(e^{x})}{128sin^{\frac{5}{2}}(e^{x})} + \frac{73655160804225e^{{x}*{11}}cos^{5}(e^{x})}{64sin^{\frac{9}{2}}(e^{x})} - \frac{86616421716825e^{{x}*{12}}cos^{4}(e^{x})}{256sin^{\frac{7}{2}}(e^{x})} - \frac{5423042181375e^{{x}*{14}}cos^{4}(e^{x})}{512sin^{\frac{7}{2}}(e^{x})} + \frac{78067776661875e^{{x}*{9}}cos^{9}(e^{x})}{256sin^{\frac{17}{2}}(e^{x})} + \frac{88764283082475e^{{x}*{13}}cos^{5}(e^{x})}{512sin^{\frac{9}{2}}(e^{x})} - \frac{41483968651125e^{{x}*{10}}cos^{8}(e^{x})}{32sin^{\frac{15}{2}}(e^{x})} - \frac{37869247941525e^{{x}*{14}}cos^{6}(e^{x})}{1024sin^{\frac{11}{2}}(e^{x})} - \frac{111581813418075e^{{x}*{12}}cos^{6}(e^{x})}{128sin^{\frac{11}{2}}(e^{x})} + \frac{218074239357975e^{{x}*{11}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} + \frac{94543679104875e^{{x}*{13}}cos^{7}(e^{x})}{256sin^{\frac{13}{2}}(e^{x})} - \frac{137414649747375e^{{x}*{14}}cos^{8}(e^{x})}{2048sin^{\frac{15}{2}}(e^{x})} - \frac{1135358089640775e^{{x}*{12}}cos^{8}(e^{x})}{1024sin^{\frac{15}{2}}(e^{x})} - \frac{24318188519625e^{{x}*{10}}cos^{10}(e^{x})}{64sin^{\frac{19}{2}}(e^{x})} + \frac{843162423728625e^{{x}*{13}}cos^{9}(e^{x})}{2048sin^{\frac{17}{2}}(e^{x})} - \frac{272674156379625e^{{x}*{14}}cos^{10}(e^{x})}{4096sin^{\frac{19}{2}}(e^{x})} + \frac{607650355186875e^{{x}*{11}}cos^{9}(e^{x})}{512sin^{\frac{17}{2}}(e^{x})} - \frac{708331916667375e^{{x}*{12}}cos^{10}(e^{x})}{1024sin^{\frac{19}{2}}(e^{x})} + \frac{476344864870875e^{{x}*{13}}cos^{11}(e^{x})}{2048sin^{\frac{21}{2}}(e^{x})} - \frac{281517134023125e^{{x}*{14}}cos^{12}(e^{x})}{8192sin^{\frac{23}{2}}(e^{x})} + \frac{324414983017125e^{{x}*{11}}cos^{11}(e^{x})}{1024sin^{\frac{21}{2}}(e^{x})} - \frac{694408930590375e^{{x}*{12}}cos^{12}(e^{x})}{4096sin^{\frac{23}{2}}(e^{x})} + \frac{431659605502125e^{{x}*{13}}cos^{13}(e^{x})}{8192sin^{\frac{25}{2}}(e^{x})} - \frac{118587803709375e^{{x}*{14}}cos^{14}(e^{x})}{16384sin^{\frac{27}{2}}(e^{x})} - \frac{4148706885e^{{x}*{14}}sin^{\frac{1}{2}}(e^{x})}{128} - \frac{155876175e^{{x}*{4}}sin^{\frac{1}{2}}(e^{x})}{4} - 10959362700e^{{x}*{8}}sin^{\frac{1}{2}}(e^{x}) - \frac{18079366305e^{{x}*{6}}sin^{\frac{1}{2}}(e^{x})}{8} - \frac{20579063505e^{{x}*{10}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{122865e^{{x}*{2}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{119599930905e^{{x}*{12}}sin^{\frac{1}{2}}(e^{x})}{64} + \frac{xe^{x}cos(e^{x})}{2sin^{\frac{1}{2}}(e^{x})} - \frac{16383xe^{{x}*{2}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{2375101xe^{{x}*{3}}cos(e^{x})}{4sin^{\frac{1}{2}}(e^{x})} + \frac{7125303xe^{{x}*{3}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{105889875xe^{{x}*{4}}cos^{2}(e^{x})}{2sin^{\frac{3}{2}}(e^{x})} + \frac{500571435xe^{{x}*{5}}cos(e^{x})}{sin^{\frac{1}{2}}(e^{x})} - \frac{317669625xe^{{x}*{4}}cos^{4}(e^{x})}{8sin^{\frac{7}{2}}(e^{x})} + \frac{1185563925xe^{{x}*{5}}cos^{3}(e^{x})}{sin^{\frac{5}{2}}(e^{x})} - \frac{121580355897xe^{{x}*{6}}cos^{2}(e^{x})}{16sin^{\frac{3}{2}}(e^{x})} + \frac{228486405147xe^{{x}*{7}}cos(e^{x})}{16sin^{\frac{1}{2}}(e^{x})} + \frac{2766315825xe^{{x}*{5}}cos^{5}(e^{x})}{4sin^{\frac{9}{2}}(e^{x})} - \frac{410175941175xe^{{x}*{6}}cos^{4}(e^{x})}{32sin^{\frac{7}{2}}(e^{x})} + \frac{1948469934411xe^{{x}*{7}}cos^{3}(e^{x})}{32sin^{\frac{5}{2}}(e^{x})} - \frac{100596553200xe^{{x}*{8}}cos^{2}(e^{x})}{sin^{\frac{3}{2}}(e^{x})} + \frac{978766948445xe^{{x}*{9}}cos(e^{x})}{16sin^{\frac{1}{2}}(e^{x})} - \frac{397555142985xe^{{x}*{6}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{5107222955835xe^{{x}*{7}}cos^{5}(e^{x})}{64sin^{\frac{9}{2}}(e^{x})} - \frac{292142951100xe^{{x}*{8}}cos^{4}(e^{x})}{sin^{\frac{7}{2}}(e^{x})} + \frac{3271003496475xe^{{x}*{9}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{7588859102825xe^{{x}*{10}}cos^{2}(e^{x})}{32sin^{\frac{3}{2}}(e^{x})} + \frac{1751761870859xe^{{x}*{11}}cos(e^{x})}{32sin^{\frac{1}{2}}(e^{x})} + \frac{4248866156535xe^{{x}*{7}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} - \frac{313467254100xe^{{x}*{8}}cos^{6}(e^{x})}{sin^{\frac{11}{2}}(e^{x})} + \frac{28789563327525xe^{{x}*{9}}cos^{5}(e^{x})}{32sin^{\frac{9}{2}}(e^{x})} - \frac{33323504589375xe^{{x}*{10}}cos^{4}(e^{x})}{32sin^{\frac{7}{2}}(e^{x})} + \frac{33807598381557xe^{{x}*{11}}cos^{3}(e^{x})}{64sin^{\frac{5}{2}}(e^{x})} - \frac{3712456381725xe^{{x}*{12}}cos^{2}(e^{x})}{32sin^{\frac{3}{2}}(e^{x})} + \frac{629220544225xe^{{x}*{13}}cos(e^{x})}{64sin^{\frac{1}{2}}(e^{x})} - \frac{228703149675xe^{{x}*{8}}cos^{8}(e^{x})}{2sin^{\frac{15}{2}}(e^{x})} + \frac{26167524508125xe^{{x}*{9}}cos^{7}(e^{x})}{32sin^{\frac{13}{2}}(e^{x})} - \frac{117980790802875xe^{{x}*{10}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{43947282079xe^{{x}*{15}}cos(e^{x})}{256sin^{\frac{1}{2}}(e^{x})} + \frac{109961947140045xe^{{x}*{11}}cos^{5}(e^{x})}{64sin^{\frac{9}{2}}(e^{x})} - \frac{91298390458275xe^{{x}*{12}}cos^{4}(e^{x})}{128sin^{\frac{7}{2}}(e^{x})} - \frac{2321752783245xe^{{x}*{14}}cos^{2}(e^{x})}{256sin^{\frac{3}{2}}(e^{x})} + \frac{8279237182125xe^{{x}*{13}}cos^{3}(e^{x})}{64sin^{\frac{5}{2}}(e^{x})} + \frac{68035563721125xe^{{x}*{9}}cos^{9}(e^{x})}{256sin^{\frac{17}{2}}(e^{x})} + \frac{1512480375507xe^{{x}*{15}}cos^{3}(e^{x})}{512sin^{\frac{5}{2}}(e^{x})} - \frac{372178867685625xe^{{x}*{10}}cos^{8}(e^{x})}{256sin^{\frac{15}{2}}(e^{x})} - \frac{37961295269625xe^{{x}*{14}}cos^{4}(e^{x})}{512sin^{\frac{7}{2}}(e^{x})} + \frac{325569419970795xe^{{x}*{11}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} + \frac{17678452194585xe^{{x}*{15}}cos^{5}(e^{x})}{1024sin^{\frac{9}{2}}(e^{x})} - \frac{117613262792025xe^{{x}*{12}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{147940471804125xe^{{x}*{13}}cos^{5}(e^{x})}{256sin^{\frac{9}{2}}(e^{x})} - \frac{265084735590675xe^{{x}*{14}}cos^{6}(e^{x})}{1024sin^{\frac{11}{2}}(e^{x})} - \frac{218173818988125xe^{{x}*{10}}cos^{10}(e^{x})}{512sin^{\frac{19}{2}}(e^{x})} + \frac{101058595022385xe^{{x}*{15}}cos^{7}(e^{x})}{2048sin^{\frac{13}{2}}(e^{x})} + \frac{157572798508125xe^{{x}*{13}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} + \frac{907179015117375xe^{{x}*{11}}cos^{9}(e^{x})}{512sin^{\frac{17}{2}}(e^{x})} - \frac{961902548231625xe^{{x}*{14}}cos^{8}(e^{x})}{2048sin^{\frac{15}{2}}(e^{x})} + \frac{319197420667125xe^{{x}*{15}}cos^{9}(e^{x})}{4096sin^{\frac{17}{2}}(e^{x})} - \frac{1196728797188925xe^{{x}*{12}}cos^{8}(e^{x})}{512sin^{\frac{15}{2}}(e^{x})} + \frac{1405270706214375xe^{{x}*{13}}cos^{9}(e^{x})}{1024sin^{\frac{17}{2}}(e^{x})} - \frac{1908719094657375xe^{{x}*{14}}cos^{10}(e^{x})}{4096sin^{\frac{19}{2}}(e^{x})} + \frac{570600971966025xe^{{x}*{15}}cos^{11}(e^{x})}{8192sin^{\frac{21}{2}}(e^{x})} + \frac{484328631211425xe^{{x}*{11}}cos^{11}(e^{x})}{1024sin^{\frac{21}{2}}(e^{x})} - \frac{746620128379125xe^{{x}*{12}}cos^{10}(e^{x})}{512sin^{\frac{19}{2}}(e^{x})} + \frac{793908108118125xe^{{x}*{13}}cos^{11}(e^{x})}{1024sin^{\frac{21}{2}}(e^{x})} - \frac{1970619938161875xe^{{x}*{14}}cos^{12}(e^{x})}{8192sin^{\frac{23}{2}}(e^{x})} + \frac{542341555630875xe^{{x}*{15}}cos^{13}(e^{x})}{16384sin^{\frac{25}{2}}(e^{x})} - \frac{731944548460125xe^{{x}*{12}}cos^{12}(e^{x})}{2048sin^{\frac{23}{2}}(e^{x})} + \frac{719432675836875xe^{{x}*{13}}cos^{13}(e^{x})}{4096sin^{\frac{25}{2}}(e^{x})} - \frac{830114625965625xe^{{x}*{14}}cos^{14}(e^{x})}{16384sin^{\frac{27}{2}}(e^{x})} + \frac{213458046676875xe^{{x}*{15}}cos^{15}(e^{x})}{32768sin^{\frac{29}{2}}(e^{x})} - 7568435160xe^{{x}*{8}}sin^{\frac{1}{2}}(e^{x}) - \frac{21177975xe^{{x}*{4}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{184627768325xe^{{x}*{10}}sin^{\frac{1}{2}}(e^{x})}{16} - \frac{7993172187xe^{{x}*{6}}sin^{\frac{1}{2}}(e^{x})}{8} - \frac{126064792035xe^{{x}*{12}}sin^{\frac{1}{2}}(e^{x})}{32} - \frac{16383xe^{{x}*{2}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{29040948195xe^{{x}*{14}}sin^{\frac{1}{2}}(e^{x})}{128}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数xsqrt(sin(e^{x})) 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 15 阶导数：} \\=&\frac{15e^{x}cos(e^{x})}{2sin^{\frac{1}{2}}(e^{x})} - \frac{122865e^{{x}*{2}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{5917275e^{{x}*{3}}cos(e^{x})}{2sin^{\frac{1}{2}}(e^{x})} + \frac{17751825e^{{x}*{3}}cos^{3}(e^{x})}{4sin^{\frac{5}{2}}(e^{x})} - \frac{779380875e^{{x}*{4}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{11421384975e^{{x}*{5}}cos(e^{x})}{8sin^{\frac{1}{2}}(e^{x})} - \frac{2338142625e^{{x}*{4}}cos^{4}(e^{x})}{16sin^{\frac{7}{2}}(e^{x})} + \frac{27050648625e^{{x}*{5}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{274996676955e^{{x}*{6}}cos^{2}(e^{x})}{16sin^{\frac{3}{2}}(e^{x})} + \frac{25851625800e^{{x}*{7}}cos(e^{x})}{sin^{\frac{1}{2}}(e^{x})} + \frac{63118180125e^{{x}*{5}}cos^{5}(e^{x})}{32sin^{\frac{9}{2}}(e^{x})} - \frac{927756955125e^{{x}*{6}}cos^{4}(e^{x})}{32sin^{\frac{7}{2}}(e^{x})} + \frac{110227817700e^{{x}*{7}}cos^{3}(e^{x})}{sin^{\frac{5}{2}}(e^{x})} - \frac{145667379000e^{{x}*{8}}cos^{2}(e^{x})}{sin^{\frac{3}{2}}(e^{x})} + \frac{1123091444475e^{{x}*{9}}cos(e^{x})}{16sin^{\frac{1}{2}}(e^{x})} - \frac{899210587275e^{{x}*{6}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{144461567250e^{{x}*{7}}cos^{5}(e^{x})}{sin^{\frac{9}{2}}(e^{x})} - \frac{423033360750e^{{x}*{8}}cos^{4}(e^{x})}{sin^{\frac{7}{2}}(e^{x})} + \frac{3753330706125e^{{x}*{9}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{845872832805e^{{x}*{10}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{1173372295095e^{{x}*{11}}cos(e^{x})}{32sin^{\frac{1}{2}}(e^{x})} + \frac{60091156125e^{{x}*{7}}cos^{7}(e^{x})}{sin^{\frac{13}{2}}(e^{x})} - \frac{453911708250e^{{x}*{8}}cos^{6}(e^{x})}{sin^{\frac{11}{2}}(e^{x})} + \frac{33034740613875e^{{x}*{9}}cos^{5}(e^{x})}{32sin^{\frac{9}{2}}(e^{x})} - \frac{3714319483875e^{{x}*{10}}cos^{4}(e^{x})}{4sin^{\frac{7}{2}}(e^{x})} + \frac{22645143706185e^{{x}*{11}}cos^{3}(e^{x})}{64sin^{\frac{5}{2}}(e^{x})} - \frac{3522074003175e^{{x}*{12}}cos^{2}(e^{x})}{64sin^{\frac{3}{2}}(e^{x})} + \frac{377532326535e^{{x}*{13}}cos(e^{x})}{128sin^{\frac{1}{2}}(e^{x})} - \frac{662340553875e^{{x}*{8}}cos^{8}(e^{x})}{4sin^{\frac{15}{2}}(e^{x})} + \frac{30026067946875e^{{x}*{9}}cos^{7}(e^{x})}{32sin^{\frac{13}{2}}(e^{x})} - \frac{331678969035e^{{x}*{14}}cos^{2}(e^{x})}{256sin^{\frac{3}{2}}(e^{x})} - \frac{13150428065775e^{{x}*{10}}cos^{6}(e^{x})}{8sin^{\frac{11}{2}}(e^{x})} + \frac{4967542309275e^{{x}*{13}}cos^{3}(e^{x})}{128sin^{\frac{5}{2}}(e^{x})} + \frac{73655160804225e^{{x}*{11}}cos^{5}(e^{x})}{64sin^{\frac{9}{2}}(e^{x})} - \frac{86616421716825e^{{x}*{12}}cos^{4}(e^{x})}{256sin^{\frac{7}{2}}(e^{x})} - \frac{5423042181375e^{{x}*{14}}cos^{4}(e^{x})}{512sin^{\frac{7}{2}}(e^{x})} + \frac{78067776661875e^{{x}*{9}}cos^{9}(e^{x})}{256sin^{\frac{17}{2}}(e^{x})} + \frac{88764283082475e^{{x}*{13}}cos^{5}(e^{x})}{512sin^{\frac{9}{2}}(e^{x})} - \frac{41483968651125e^{{x}*{10}}cos^{8}(e^{x})}{32sin^{\frac{15}{2}}(e^{x})} - \frac{37869247941525e^{{x}*{14}}cos^{6}(e^{x})}{1024sin^{\frac{11}{2}}(e^{x})} - \frac{111581813418075e^{{x}*{12}}cos^{6}(e^{x})}{128sin^{\frac{11}{2}}(e^{x})} + \frac{218074239357975e^{{x}*{11}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} + \frac{94543679104875e^{{x}*{13}}cos^{7}(e^{x})}{256sin^{\frac{13}{2}}(e^{x})} - \frac{137414649747375e^{{x}*{14}}cos^{8}(e^{x})}{2048sin^{\frac{15}{2}}(e^{x})} - \frac{1135358089640775e^{{x}*{12}}cos^{8}(e^{x})}{1024sin^{\frac{15}{2}}(e^{x})} - \frac{24318188519625e^{{x}*{10}}cos^{10}(e^{x})}{64sin^{\frac{19}{2}}(e^{x})} + \frac{843162423728625e^{{x}*{13}}cos^{9}(e^{x})}{2048sin^{\frac{17}{2}}(e^{x})} - \frac{272674156379625e^{{x}*{14}}cos^{10}(e^{x})}{4096sin^{\frac{19}{2}}(e^{x})} + \frac{607650355186875e^{{x}*{11}}cos^{9}(e^{x})}{512sin^{\frac{17}{2}}(e^{x})} - \frac{708331916667375e^{{x}*{12}}cos^{10}(e^{x})}{1024sin^{\frac{19}{2}}(e^{x})} + \frac{476344864870875e^{{x}*{13}}cos^{11}(e^{x})}{2048sin^{\frac{21}{2}}(e^{x})} - \frac{281517134023125e^{{x}*{14}}cos^{12}(e^{x})}{8192sin^{\frac{23}{2}}(e^{x})} + \frac{324414983017125e^{{x}*{11}}cos^{11}(e^{x})}{1024sin^{\frac{21}{2}}(e^{x})} - \frac{694408930590375e^{{x}*{12}}cos^{12}(e^{x})}{4096sin^{\frac{23}{2}}(e^{x})} + \frac{431659605502125e^{{x}*{13}}cos^{13}(e^{x})}{8192sin^{\frac{25}{2}}(e^{x})} - \frac{118587803709375e^{{x}*{14}}cos^{14}(e^{x})}{16384sin^{\frac{27}{2}}(e^{x})} - \frac{4148706885e^{{x}*{14}}sin^{\frac{1}{2}}(e^{x})}{128} - \frac{155876175e^{{x}*{4}}sin^{\frac{1}{2}}(e^{x})}{4} - 10959362700e^{{x}*{8}}sin^{\frac{1}{2}}(e^{x}) - \frac{18079366305e^{{x}*{6}}sin^{\frac{1}{2}}(e^{x})}{8} - \frac{20579063505e^{{x}*{10}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{122865e^{{x}*{2}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{119599930905e^{{x}*{12}}sin^{\frac{1}{2}}(e^{x})}{64} + \frac{xe^{x}cos(e^{x})}{2sin^{\frac{1}{2}}(e^{x})} - \frac{16383xe^{{x}*{2}}cos^{2}(e^{x})}{4sin^{\frac{3}{2}}(e^{x})} + \frac{2375101xe^{{x}*{3}}cos(e^{x})}{4sin^{\frac{1}{2}}(e^{x})} + \frac{7125303xe^{{x}*{3}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{105889875xe^{{x}*{4}}cos^{2}(e^{x})}{2sin^{\frac{3}{2}}(e^{x})} + \frac{500571435xe^{{x}*{5}}cos(e^{x})}{sin^{\frac{1}{2}}(e^{x})} - \frac{317669625xe^{{x}*{4}}cos^{4}(e^{x})}{8sin^{\frac{7}{2}}(e^{x})} + \frac{1185563925xe^{{x}*{5}}cos^{3}(e^{x})}{sin^{\frac{5}{2}}(e^{x})} - \frac{121580355897xe^{{x}*{6}}cos^{2}(e^{x})}{16sin^{\frac{3}{2}}(e^{x})} + \frac{228486405147xe^{{x}*{7}}cos(e^{x})}{16sin^{\frac{1}{2}}(e^{x})} + \frac{2766315825xe^{{x}*{5}}cos^{5}(e^{x})}{4sin^{\frac{9}{2}}(e^{x})} - \frac{410175941175xe^{{x}*{6}}cos^{4}(e^{x})}{32sin^{\frac{7}{2}}(e^{x})} + \frac{1948469934411xe^{{x}*{7}}cos^{3}(e^{x})}{32sin^{\frac{5}{2}}(e^{x})} - \frac{100596553200xe^{{x}*{8}}cos^{2}(e^{x})}{sin^{\frac{3}{2}}(e^{x})} + \frac{978766948445xe^{{x}*{9}}cos(e^{x})}{16sin^{\frac{1}{2}}(e^{x})} - \frac{397555142985xe^{{x}*{6}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{5107222955835xe^{{x}*{7}}cos^{5}(e^{x})}{64sin^{\frac{9}{2}}(e^{x})} - \frac{292142951100xe^{{x}*{8}}cos^{4}(e^{x})}{sin^{\frac{7}{2}}(e^{x})} + \frac{3271003496475xe^{{x}*{9}}cos^{3}(e^{x})}{8sin^{\frac{5}{2}}(e^{x})} - \frac{7588859102825xe^{{x}*{10}}cos^{2}(e^{x})}{32sin^{\frac{3}{2}}(e^{x})} + \frac{1751761870859xe^{{x}*{11}}cos(e^{x})}{32sin^{\frac{1}{2}}(e^{x})} + \frac{4248866156535xe^{{x}*{7}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} - \frac{313467254100xe^{{x}*{8}}cos^{6}(e^{x})}{sin^{\frac{11}{2}}(e^{x})} + \frac{28789563327525xe^{{x}*{9}}cos^{5}(e^{x})}{32sin^{\frac{9}{2}}(e^{x})} - \frac{33323504589375xe^{{x}*{10}}cos^{4}(e^{x})}{32sin^{\frac{7}{2}}(e^{x})} + \frac{33807598381557xe^{{x}*{11}}cos^{3}(e^{x})}{64sin^{\frac{5}{2}}(e^{x})} - \frac{3712456381725xe^{{x}*{12}}cos^{2}(e^{x})}{32sin^{\frac{3}{2}}(e^{x})} + \frac{629220544225xe^{{x}*{13}}cos(e^{x})}{64sin^{\frac{1}{2}}(e^{x})} - \frac{228703149675xe^{{x}*{8}}cos^{8}(e^{x})}{2sin^{\frac{15}{2}}(e^{x})} + \frac{26167524508125xe^{{x}*{9}}cos^{7}(e^{x})}{32sin^{\frac{13}{2}}(e^{x})} - \frac{117980790802875xe^{{x}*{10}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{43947282079xe^{{x}*{15}}cos(e^{x})}{256sin^{\frac{1}{2}}(e^{x})} + \frac{109961947140045xe^{{x}*{11}}cos^{5}(e^{x})}{64sin^{\frac{9}{2}}(e^{x})} - \frac{91298390458275xe^{{x}*{12}}cos^{4}(e^{x})}{128sin^{\frac{7}{2}}(e^{x})} - \frac{2321752783245xe^{{x}*{14}}cos^{2}(e^{x})}{256sin^{\frac{3}{2}}(e^{x})} + \frac{8279237182125xe^{{x}*{13}}cos^{3}(e^{x})}{64sin^{\frac{5}{2}}(e^{x})} + \frac{68035563721125xe^{{x}*{9}}cos^{9}(e^{x})}{256sin^{\frac{17}{2}}(e^{x})} + \frac{1512480375507xe^{{x}*{15}}cos^{3}(e^{x})}{512sin^{\frac{5}{2}}(e^{x})} - \frac{372178867685625xe^{{x}*{10}}cos^{8}(e^{x})}{256sin^{\frac{15}{2}}(e^{x})} - \frac{37961295269625xe^{{x}*{14}}cos^{4}(e^{x})}{512sin^{\frac{7}{2}}(e^{x})} + \frac{325569419970795xe^{{x}*{11}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} + \frac{17678452194585xe^{{x}*{15}}cos^{5}(e^{x})}{1024sin^{\frac{9}{2}}(e^{x})} - \frac{117613262792025xe^{{x}*{12}}cos^{6}(e^{x})}{64sin^{\frac{11}{2}}(e^{x})} + \frac{147940471804125xe^{{x}*{13}}cos^{5}(e^{x})}{256sin^{\frac{9}{2}}(e^{x})} - \frac{265084735590675xe^{{x}*{14}}cos^{6}(e^{x})}{1024sin^{\frac{11}{2}}(e^{x})} - \frac{218173818988125xe^{{x}*{10}}cos^{10}(e^{x})}{512sin^{\frac{19}{2}}(e^{x})} + \frac{101058595022385xe^{{x}*{15}}cos^{7}(e^{x})}{2048sin^{\frac{13}{2}}(e^{x})} + \frac{157572798508125xe^{{x}*{13}}cos^{7}(e^{x})}{128sin^{\frac{13}{2}}(e^{x})} + \frac{907179015117375xe^{{x}*{11}}cos^{9}(e^{x})}{512sin^{\frac{17}{2}}(e^{x})} - \frac{961902548231625xe^{{x}*{14}}cos^{8}(e^{x})}{2048sin^{\frac{15}{2}}(e^{x})} + \frac{319197420667125xe^{{x}*{15}}cos^{9}(e^{x})}{4096sin^{\frac{17}{2}}(e^{x})} - \frac{1196728797188925xe^{{x}*{12}}cos^{8}(e^{x})}{512sin^{\frac{15}{2}}(e^{x})} + \frac{1405270706214375xe^{{x}*{13}}cos^{9}(e^{x})}{1024sin^{\frac{17}{2}}(e^{x})} - \frac{1908719094657375xe^{{x}*{14}}cos^{10}(e^{x})}{4096sin^{\frac{19}{2}}(e^{x})} + \frac{570600971966025xe^{{x}*{15}}cos^{11}(e^{x})}{8192sin^{\frac{21}{2}}(e^{x})} + \frac{484328631211425xe^{{x}*{11}}cos^{11}(e^{x})}{1024sin^{\frac{21}{2}}(e^{x})} - \frac{746620128379125xe^{{x}*{12}}cos^{10}(e^{x})}{512sin^{\frac{19}{2}}(e^{x})} + \frac{793908108118125xe^{{x}*{13}}cos^{11}(e^{x})}{1024sin^{\frac{21}{2}}(e^{x})} - \frac{1970619938161875xe^{{x}*{14}}cos^{12}(e^{x})}{8192sin^{\frac{23}{2}}(e^{x})} + \frac{542341555630875xe^{{x}*{15}}cos^{13}(e^{x})}{16384sin^{\frac{25}{2}}(e^{x})} - \frac{731944548460125xe^{{x}*{12}}cos^{12}(e^{x})}{2048sin^{\frac{23}{2}}(e^{x})} + \frac{719432675836875xe^{{x}*{13}}cos^{13}(e^{x})}{4096sin^{\frac{25}{2}}(e^{x})} - \frac{830114625965625xe^{{x}*{14}}cos^{14}(e^{x})}{16384sin^{\frac{27}{2}}(e^{x})} + \frac{213458046676875xe^{{x}*{15}}cos^{15}(e^{x})}{32768sin^{\frac{29}{2}}(e^{x})} - 7568435160xe^{{x}*{8}}sin^{\frac{1}{2}}(e^{x}) - \frac{21177975xe^{{x}*{4}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{184627768325xe^{{x}*{10}}sin^{\frac{1}{2}}(e^{x})}{16} - \frac{7993172187xe^{{x}*{6}}sin^{\frac{1}{2}}(e^{x})}{8} - \frac{126064792035xe^{{x}*{12}}sin^{\frac{1}{2}}(e^{x})}{32} - \frac{16383xe^{{x}*{2}}sin^{\frac{1}{2}}(e^{x})}{2} - \frac{29040948195xe^{{x}*{14}}sin^{\frac{1}{2}}(e^{x})}{128}\\ \end{split}\end{equation} \]
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