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 2 questions in this calculation: for each question, the 6 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/2]Find\ the\ 6th\ derivative\ of\ function\ 9xy + x{y}^{2} + sin(\frac{π}{(x + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 9yx + y^{2}x + sin(\frac{π}{(x + 1)})\\\\ &\color{blue}{The\ 6th\ derivative\ of\ function:} \\=&\frac{720πcos(\frac{π}{(x + 1)})}{(x + 1)^{7}} - \frac{1800π^{2}sin(\frac{π}{(x + 1)})}{(x + 1)^{8}} - \frac{1200π^{3}cos(\frac{π}{(x + 1)})}{(x + 1)^{9}} + \frac{300π^{4}sin(\frac{π}{(x + 1)})}{(x + 1)^{10}} + \frac{30π^{5}cos(\frac{π}{(x + 1)})}{(x + 1)^{11}} - \frac{π^{6}sin(\frac{π}{(x + 1)})}{(x + 1)^{12}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[2/2]Find\ the\ 6th\ derivative\ of\ function\ 98i{x}^{4} + arccos(9{x}^{2} - sqrt(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 98ix^{4} + arccos(9x^{2} - sqrt(x))\\\\ &\color{blue}{The\ 6th\ derivative\ of\ function:} \\=&\frac{32141551680x^{6}sqrt(x)^{5}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{80353879200x^{\frac{13}{2}}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{5580130500x^{5}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{2976069600x^{4}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{220973167800x^{7}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{9486221850x^{\frac{11}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{5803335720x^{\frac{9}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{892820880x^{\frac{9}{2}}sqrt(x)^{5}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{372008700x^{4}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{326540970x^{3}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{70858800x^{2}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{1446369825600x^{8}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{124002900x^{\frac{7}{2}}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{200884698000x^{\frac{15}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{23715554625x^{6}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{14210732340x^{5}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{41334300x^{\frac{5}{2}}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{142851340800x^{6}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{26034656860800x^{10}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{837019575x^{\frac{9}{2}}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{436076865x^{\frac{7}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{120459960x^{\frac{5}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{2169554738400x^{\frac{17}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{6889050x^{\frac{5}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{24111675x^{3}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{24877125x^{2}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{328050x^{\frac{1}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{7512345xsqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{3254332107600x^{9}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{2410616376000x^{8}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{3061800x^{\frac{3}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{165171862800x^{\frac{13}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{234311911747200x^{12}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{4464104400x^{4}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{262440sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{26034656860800x^{\frac{21}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{382725x^{\frac{3}{2}}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{18225sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x^{\frac{1}{2}}} - \frac{3645sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{3}{2}}} + \frac{191398476150x^{7}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{494678568825x^{8}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{98489303325x^{\frac{13}{2}}sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{20156671395x^{\frac{11}{2}}sqrt(x)}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1085025375x^{5}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{3831000705x^{4}sqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1055304045x^{3}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{3994664850x^{\frac{9}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{127575x^{\frac{1}{2}}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{21153158699400x^{11}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{17356437907200x^{10}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{65445975x^{\frac{7}{2}}sqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{45544275x^{\frac{5}{2}}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{80842455x^{\frac{3}{2}}sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{1707519933000x^{\frac{17}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1054403602862400x^{14}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{2355399x^{\frac{1}{2}}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{70787941200x^{6}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{1672365110850x^{\frac{19}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{146444944842000x^{\frac{25}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{47239200x^{2}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{382725x^{2}sqrt(x)}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{1573425xsqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{48600sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{42525x^{\frac{1}{2}}sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{8019sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x} - \frac{2025sqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x^{\frac{3}{2}}} + \frac{405sqrt(x)}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{5}{2}}} - \frac{2025sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}x^{\frac{7}{2}}} + \frac{212435568135x^{\frac{17}{2}}}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{94918019805x^{7}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{48218527665x^{6}}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{1694964639375x^{10}}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{17256381345x^{\frac{9}{2}}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{428094315x^{2}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{1621583955x^{\frac{7}{2}}}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{167124908475x^{\frac{15}{2}}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{3999093525x^{\frac{11}{2}}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{51255730694700x^{13}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{4881498161400x^{\frac{23}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{6237469872900x^{\frac{21}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{316321080858720x^{\frac{29}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{82377}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{1}{2}}} - \frac{944158080600x^{9}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{72335025x^{4}}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{33480783000x^{\frac{13}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{7092441x}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{155003625x^{\frac{5}{2}}}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} - \frac{15309929475x^{5}}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{5327775x^{\frac{1}{2}}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{270586575x^{3}}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1913625x^{\frac{5}{2}}}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{45560649506400x^{12}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{405}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}x^{3}} + \frac{1215}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{2}} - \frac{2025}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x} - \frac{327155079600x^{8}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{2338875x^{\frac{3}{2}}}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{76545x}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{1897926485152320x^{16}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{658986840x^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} - \frac{945}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{1}{2}}x^{\frac{11}{2}}} + \frac{525}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}x^{\frac{9}{2}}} - \frac{225}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{7}{2}}} + \frac{225}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x^{\frac{5}{2}}} - \frac{525}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}x^{\frac{3}{2}}} + \frac{945}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}x^{\frac{1}{2}}} - \frac{87480}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}} - \frac{42525}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/2]Find\ the\ 6th\ derivative\ of\ function\ 9xy + x{y}^{2} + sin(\frac{π}{(x + 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 9yx + y^{2}x + sin(\frac{π}{(x + 1)})\\\\ &\color{blue}{The\ 6th\ derivative\ of\ function:} \\=&\frac{720πcos(\frac{π}{(x + 1)})}{(x + 1)^{7}} - \frac{1800π^{2}sin(\frac{π}{(x + 1)})}{(x + 1)^{8}} - \frac{1200π^{3}cos(\frac{π}{(x + 1)})}{(x + 1)^{9}} + \frac{300π^{4}sin(\frac{π}{(x + 1)})}{(x + 1)^{10}} + \frac{30π^{5}cos(\frac{π}{(x + 1)})}{(x + 1)^{11}} - \frac{π^{6}sin(\frac{π}{(x + 1)})}{(x + 1)^{12}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[2/2]Find\ the\ 6th\ derivative\ of\ function\ 98i{x}^{4} + arccos(9{x}^{2} - sqrt(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 98ix^{4} + arccos(9x^{2} - sqrt(x))\\\\ &\color{blue}{The\ 6th\ derivative\ of\ function:} \\=&\frac{32141551680x^{6}sqrt(x)^{5}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{80353879200x^{\frac{13}{2}}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{5580130500x^{5}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{2976069600x^{4}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{220973167800x^{7}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{9486221850x^{\frac{11}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{5803335720x^{\frac{9}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{892820880x^{\frac{9}{2}}sqrt(x)^{5}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{372008700x^{4}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{326540970x^{3}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{70858800x^{2}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{1446369825600x^{8}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{124002900x^{\frac{7}{2}}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{200884698000x^{\frac{15}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{23715554625x^{6}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{14210732340x^{5}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{41334300x^{\frac{5}{2}}sqrt(x)^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{142851340800x^{6}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{26034656860800x^{10}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{837019575x^{\frac{9}{2}}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{436076865x^{\frac{7}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{120459960x^{\frac{5}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{2169554738400x^{\frac{17}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{6889050x^{\frac{5}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{24111675x^{3}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{24877125x^{2}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{328050x^{\frac{1}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{7512345xsqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{3254332107600x^{9}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{2410616376000x^{8}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{3061800x^{\frac{3}{2}}sqrt(x)^{3}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{165171862800x^{\frac{13}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{234311911747200x^{12}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{4464104400x^{4}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{262440sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{26034656860800x^{\frac{21}{2}}sqrt(x)^{2}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{382725x^{\frac{3}{2}}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{18225sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x^{\frac{1}{2}}} - \frac{3645sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{3}{2}}} + \frac{191398476150x^{7}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{494678568825x^{8}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{98489303325x^{\frac{13}{2}}sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{20156671395x^{\frac{11}{2}}sqrt(x)}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1085025375x^{5}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{3831000705x^{4}sqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1055304045x^{3}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{3994664850x^{\frac{9}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{127575x^{\frac{1}{2}}sqrt(x)^{2}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{21153158699400x^{11}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{17356437907200x^{10}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{65445975x^{\frac{7}{2}}sqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{45544275x^{\frac{5}{2}}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{80842455x^{\frac{3}{2}}sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{1707519933000x^{\frac{17}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1054403602862400x^{14}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{2355399x^{\frac{1}{2}}sqrt(x)}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{70787941200x^{6}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{1672365110850x^{\frac{19}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{146444944842000x^{\frac{25}{2}}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{47239200x^{2}sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{382725x^{2}sqrt(x)}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{1573425xsqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{48600sqrt(x)}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{42525x^{\frac{1}{2}}sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{8019sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x} - \frac{2025sqrt(x)}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x^{\frac{3}{2}}} + \frac{405sqrt(x)}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{5}{2}}} - \frac{2025sqrt(x)}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}x^{\frac{7}{2}}} + \frac{212435568135x^{\frac{17}{2}}}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{94918019805x^{7}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{48218527665x^{6}}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{1694964639375x^{10}}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{17256381345x^{\frac{9}{2}}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{428094315x^{2}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{1621583955x^{\frac{7}{2}}}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{167124908475x^{\frac{15}{2}}}{2(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{3999093525x^{\frac{11}{2}}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{51255730694700x^{13}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{4881498161400x^{\frac{23}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{6237469872900x^{\frac{21}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{316321080858720x^{\frac{29}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{82377}{8(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{1}{2}}} - \frac{944158080600x^{9}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{72335025x^{4}}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} + \frac{33480783000x^{\frac{13}{2}}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{7092441x}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} + \frac{155003625x^{\frac{5}{2}}}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} - \frac{15309929475x^{5}}{4(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{5327775x^{\frac{1}{2}}}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} - \frac{270586575x^{3}}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} + \frac{1913625x^{\frac{5}{2}}}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{45560649506400x^{12}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{405}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}x^{3}} + \frac{1215}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{2}} - \frac{2025}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x} - \frac{327155079600x^{8}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}} + \frac{2338875x^{\frac{3}{2}}}{16(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}} - \frac{76545x}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{1897926485152320x^{16}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}} - \frac{658986840x^{4}}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}} - \frac{945}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{1}{2}}x^{\frac{11}{2}}} + \frac{525}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}x^{\frac{9}{2}}} - \frac{225}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{5}{2}}x^{\frac{7}{2}}} + \frac{225}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{7}{2}}x^{\frac{5}{2}}} - \frac{525}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}x^{\frac{3}{2}}} + \frac{945}{64(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{11}{2}}x^{\frac{1}{2}}} - \frac{87480}{(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{3}{2}}} - \frac{42525}{32(18x^{2}sqrt(x) - 81x^{4} - sqrt(x)^{2} + 1)^{\frac{9}{2}}}\\ \end{split}\end{equation} \]