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 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{sqrt(9 - x)}^{ - \frac{3}{sin(2x)}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}\right)}{dx}\\=&(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})\\=&\frac{-2cos(2x)}{ln(sqrt(-x + 9))sin(2x)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2(-x + 9)^{\frac{1}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2cos(2x)}{ln(sqrt(-x + 9))sin(2x)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2(-x + 9)^{\frac{1}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)}\right)}{dx}\\=&\frac{-2*-(-1 + 0)*\frac{1}{2}cos(2x)}{ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin(2x)} - \frac{2*-cos(2x)*2cos(2x)}{ln(sqrt(-x + 9))sin^{2}(2x)} - \frac{2*-sin(2x)*2}{ln(sqrt(-x + 9))sin(2x)} + \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 9)^{\frac{3}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{2(-x + 9)^{\frac{1}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{2(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{2(-x + 9)^{\frac{1}{2}}ln(sqrt(-x + 9))(-x + 9)(-x + 9)^{\frac{1}{2}}}\\=&\frac{-2cos(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} + \frac{4cos^{2}(2x)}{ln(sqrt(-x + 9))sin^{2}(2x)} + \frac{4}{ln(sqrt(-x + 9))} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{3}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2(-x + 9)ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{2}ln(sqrt(-x + 9))}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2cos(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} + \frac{4cos^{2}(2x)}{ln(sqrt(-x + 9))sin^{2}(2x)} + \frac{4}{ln(sqrt(-x + 9))} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{3}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2(-x + 9)ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{2}ln(sqrt(-x + 9))}\right)}{dx}\\=&\frac{-2(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 9)^{\frac{3}{2}}})cos(2x)}{ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{2*-2(-1 + 0)*\frac{1}{2}cos(2x)}{(-x + 9)^{\frac{1}{2}}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin(2x)sqrt(-x + 9)} - \frac{2*-cos(2x)*2cos(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)} - \frac{2*-sin(2x)*2}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{2cos(2x)*-(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin(2x)(-x + 9)(-x + 9)^{\frac{1}{2}}} + \frac{4*-(-1 + 0)*\frac{1}{2}cos^{2}(2x)}{ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin^{2}(2x)} + \frac{4*-2cos(2x)*2cos^{2}(2x)}{ln(sqrt(-x + 9))sin^{3}(2x)} + \frac{4*-2cos(2x)sin(2x)*2}{ln(sqrt(-x + 9))sin^{2}(2x)} + \frac{4*-(-1 + 0)*\frac{1}{2}}{ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}} + \frac{(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 9)^{\frac{5}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{4(-x + 9)^{\frac{3}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{\frac{3}{2}}ln(sqrt(-x + 9))(-x + 9)(-x + 9)^{\frac{1}{2}}} + \frac{(\frac{-(-1 + 0)}{(-x + 9)^{2}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{2(-x + 9)ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-2(-1 + 0)*\frac{1}{2}}{2(-x + 9)ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)^{2}} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-2(-1 + 0)*\frac{1}{2}}{2(-x + 9)ln^{2}(sqrt(-x + 9))(-x + 9)^{\frac{3}{2}}(-x + 9)^{\frac{1}{2}}} + \frac{(\frac{-2(-1 + 0)}{(-x + 9)^{3}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4ln(sqrt(-x + 9))} + \frac{(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{4(-x + 9)^{2}ln(sqrt(-x + 9))} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{2}ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}}\\=&\frac{-3cos(2x)}{2(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{3cos(2x)}{(-x + 9)ln^{3}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)^{2}} + \frac{6cos^{2}(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)} + \frac{6}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} - \frac{3cos(2x)}{2(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sin(2x)} - \frac{16cos^{3}(2x)}{ln(sqrt(-x + 9))sin^{3}(2x)} - \frac{16cos(2x)}{ln(sqrt(-x + 9))sin(2x)} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{\frac{5}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{3}{2}}ln^{3}(sqrt(-x + 9))sqrt(-x + 9)^{3}} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{5}{2}}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2(-x + 9)^{3}ln^{2}(sqrt(-x + 9))} + \frac{5log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{3}ln(sqrt(-x + 9))}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3cos(2x)}{2(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{3cos(2x)}{(-x + 9)ln^{3}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)^{2}} + \frac{6cos^{2}(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)} + \frac{6}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} - \frac{3cos(2x)}{2(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sin(2x)} - \frac{16cos^{3}(2x)}{ln(sqrt(-x + 9))sin^{3}(2x)} - \frac{16cos(2x)}{ln(sqrt(-x + 9))sin(2x)} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{\frac{5}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{3}{2}}ln^{3}(sqrt(-x + 9))sqrt(-x + 9)^{3}} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{5}{2}}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2(-x + 9)^{3}ln^{2}(sqrt(-x + 9))} + \frac{5log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{3}ln(sqrt(-x + 9))}\right)}{dx}\\=&\frac{-3(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 9)^{\frac{5}{2}}})cos(2x)}{2ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{3*-2(-1 + 0)*\frac{1}{2}cos(2x)}{2(-x + 9)^{\frac{3}{2}}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin(2x)sqrt(-x + 9)} - \frac{3*-cos(2x)*2cos(2x)}{2(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)} - \frac{3*-sin(2x)*2}{2(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{3cos(2x)*-(-1 + 0)*\frac{1}{2}}{2(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))sin(2x)(-x + 9)(-x + 9)^{\frac{1}{2}}} - \frac{3(\frac{-(-1 + 0)}{(-x + 9)^{2}})cos(2x)}{ln^{3}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)^{2}} - \frac{3*-3(-1 + 0)*\frac{1}{2}cos(2x)}{(-x + 9)ln^{4}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin(2x)sqrt(-x + 9)^{2}} - \frac{3*-cos(2x)*2cos(2x)}{(-x + 9)ln^{3}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)^{2}} - \frac{3*-sin(2x)*2}{(-x + 9)ln^{3}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)^{2}} - \frac{3cos(2x)*-2(-1 + 0)*\frac{1}{2}}{(-x + 9)ln^{3}(sqrt(-x + 9))sin(2x)(-x + 9)^{\frac{3}{2}}(-x + 9)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 9)^{\frac{3}{2}}})cos^{2}(2x)}{ln^{2}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)} + \frac{6*-2(-1 + 0)*\frac{1}{2}cos^{2}(2x)}{(-x + 9)^{\frac{1}{2}}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin^{2}(2x)sqrt(-x + 9)} + \frac{6*-2cos(2x)*2cos^{2}(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin^{3}(2x)sqrt(-x + 9)} + \frac{6*-2cos(2x)sin(2x)*2}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)} + \frac{6cos^{2}(2x)*-(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin^{2}(2x)(-x + 9)(-x + 9)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 9)^{\frac{3}{2}}})}{ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} + \frac{6*-2(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)} + \frac{6*-(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))(-x + 9)(-x + 9)^{\frac{1}{2}}} - \frac{3(\frac{-2(-1 + 0)}{(-x + 9)^{3}})cos(2x)}{2ln^{2}(sqrt(-x + 9))sin(2x)} - \frac{3*-2(-1 + 0)*\frac{1}{2}cos(2x)}{2(-x + 9)^{2}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin(2x)} - \frac{3*-cos(2x)*2cos(2x)}{2(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sin^{2}(2x)} - \frac{3*-sin(2x)*2}{2(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sin(2x)} - \frac{16*-(-1 + 0)*\frac{1}{2}cos^{3}(2x)}{ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin^{3}(2x)} - \frac{16*-3cos(2x)*2cos^{3}(2x)}{ln(sqrt(-x + 9))sin^{4}(2x)} - \frac{16*-3cos^{2}(2x)sin(2x)*2}{ln(sqrt(-x + 9))sin^{3}(2x)} - \frac{16*-(-1 + 0)*\frac{1}{2}cos(2x)}{ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sin(2x)} - \frac{16*-cos(2x)*2cos(2x)}{ln(sqrt(-x + 9))sin^{2}(2x)} - \frac{16*-sin(2x)*2}{ln(sqrt(-x + 9))sin(2x)} + \frac{3(\frac{\frac{-5}{2}(-1 + 0)}{(-x + 9)^{\frac{7}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{3(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{8(-x + 9)^{\frac{5}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{8(-x + 9)^{\frac{5}{2}}ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{8(-x + 9)^{\frac{5}{2}}ln(sqrt(-x + 9))(-x + 9)(-x + 9)^{\frac{1}{2}}} + \frac{3(\frac{-2(-1 + 0)}{(-x + 9)^{3}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{3(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{4(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-2(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{2}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)^{2}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-2(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{2}ln^{2}(sqrt(-x + 9))(-x + 9)^{\frac{3}{2}}(-x + 9)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 9)^{\frac{5}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4ln^{3}(sqrt(-x + 9))sqrt(-x + 9)^{3}} + \frac{3(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{4(-x + 9)^{\frac{3}{2}}ln^{3}(sqrt(-x + 9))sqrt(-x + 9)^{3}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-3(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{\frac{3}{2}}ln^{4}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)^{3}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-3(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{\frac{3}{2}}ln^{3}(sqrt(-x + 9))(-x + 9)^{2}(-x + 9)^{\frac{1}{2}}} + \frac{(\frac{\frac{-5}{2}(-1 + 0)}{(-x + 9)^{\frac{7}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} + \frac{(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{4(-x + 9)^{\frac{5}{2}}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-2(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{\frac{5}{2}}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}sqrt(-x + 9)} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{4(-x + 9)^{\frac{5}{2}}ln^{2}(sqrt(-x + 9))(-x + 9)(-x + 9)^{\frac{1}{2}}} + \frac{(\frac{-3(-1 + 0)}{(-x + 9)^{4}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2ln^{2}(sqrt(-x + 9))} + \frac{(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{2(-x + 9)^{3}ln^{2}(sqrt(-x + 9))} + \frac{log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-2(-1 + 0)*\frac{1}{2}}{2(-x + 9)^{3}ln^{3}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}} + \frac{5(\frac{-3(-1 + 0)}{(-x + 9)^{4}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8ln(sqrt(-x + 9))} + \frac{5(\frac{(\frac{(\frac{3*-cos(2x)*2}{sin^{2}(2x)})}{(\frac{3}{sin(2x)})} - \frac{(\frac{(-1 + 0)*\frac{1}{2}}{(-x + 9)^{\frac{1}{2}}})log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{(sqrt(-x + 9))})}{(ln(sqrt(-x + 9)))})}{8(-x + 9)^{3}ln(sqrt(-x + 9))} + \frac{5log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}*-(-1 + 0)*\frac{1}{2}}{8(-x + 9)^{3}ln^{2}(sqrt(-x + 9))(sqrt(-x + 9))(-x + 9)^{\frac{1}{2}}}\\=&\frac{-3cos(2x)}{(-x + 9)^{\frac{5}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{6cos(2x)}{(-x + 9)^{2}ln^{3}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)^{2}} + \frac{6cos^{2}(2x)}{(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)} + \frac{6}{(-x + 9)^{\frac{3}{2}}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} - \frac{6cos(2x)}{(-x + 9)^{\frac{3}{2}}ln^{4}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)^{3}} + \frac{12cos^{2}(2x)}{(-x + 9)ln^{3}(sqrt(-x + 9))sin^{2}(2x)sqrt(-x + 9)^{2}} - \frac{32cos^{3}(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin^{3}(2x)sqrt(-x + 9)} + \frac{12}{(-x + 9)ln^{3}(sqrt(-x + 9))sqrt(-x + 9)^{2}} - \frac{32cos(2x)}{(-x + 9)^{\frac{1}{2}}ln^{2}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{2cos(2x)}{(-x + 9)^{\frac{5}{2}}ln^{3}(sqrt(-x + 9))sin(2x)sqrt(-x + 9)} - \frac{4cos(2x)}{(-x + 9)^{3}ln^{3}(sqrt(-x + 9))sin(2x)} + \frac{6cos^{2}(2x)}{(-x + 9)^{2}ln^{2}(sqrt(-x + 9))sin^{2}(2x)} - \frac{5cos(2x)}{(-x + 9)^{3}ln^{2}(sqrt(-x + 9))sin(2x)} + \frac{6}{(-x + 9)^{2}ln^{2}(sqrt(-x + 9))} + \frac{96cos^{4}(2x)}{ln(sqrt(-x + 9))sin^{4}(2x)} + \frac{128cos^{2}(2x)}{ln(sqrt(-x + 9))sin^{2}(2x)} + \frac{32}{ln(sqrt(-x + 9))} + \frac{15log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{16(-x + 9)^{\frac{7}{2}}ln(sqrt(-x + 9))sqrt(-x + 9)} + \frac{15log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{3}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{9log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{5}{2}}ln^{3}(sqrt(-x + 9))sqrt(-x + 9)^{3}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{2(-x + 9)^{2}ln^{4}(sqrt(-x + 9))sqrt(-x + 9)^{4}} + \frac{5log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{7}{2}}ln^{2}(sqrt(-x + 9))sqrt(-x + 9)} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{3}ln^{3}(sqrt(-x + 9))sqrt(-x + 9)^{2}} + \frac{3log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{4(-x + 9)^{\frac{7}{2}}ln^{3}(sqrt(-x + 9))sqrt(-x + 9)} + \frac{19log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{4}ln^{2}(sqrt(-x + 9))} + \frac{33log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{16(-x + 9)^{4}ln(sqrt(-x + 9))} + \frac{9log_{sqrt(-x + 9)}^{ - \frac{3}{sin(2x)}}}{8(-x + 9)^{4}ln^{3}(sqrt(-x + 9))}\\ \end{split}\end{equation} \]