本次共计算 1 个题目：每一题对 x 求 4 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数8e^{4x - \frac{9sin(3x)}{(4x)}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 8e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 8e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\right)}{dx}\\=&8e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)\\=&\frac{18e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} - \frac{54e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x} + 32e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{18e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} - \frac{54e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x} + 32e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\right)}{dx}\\=&\frac{18*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} + \frac{18e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x^{2}} + \frac{18e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x^{2}} - \frac{54*-e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} - \frac{54e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos(3x)}{x} - \frac{54e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-sin(3x)*3}{x} + 32e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)\\=& - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{3}} + \frac{81e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{2x^{4}} - \frac{36e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} + \frac{144e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{2x^{2}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x} + \frac{162e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x} + 128e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{3}} + \frac{81e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{2x^{4}} - \frac{36e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} + \frac{144e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{2x^{2}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x} + \frac{162e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x} + 128e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\right)}{dx}\\=& - \frac{243*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{4}} - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)cos(3x)}{x^{3}} - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3cos(3x)}{x^{3}} - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)*-sin(3x)*3}{x^{3}} + \frac{81*-4e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{2x^{5}} + \frac{81e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin^{2}(3x)}{2x^{4}} + \frac{81e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*2sin(3x)cos(3x)*3}{2x^{4}} - \frac{36*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{4}} - \frac{36e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x^{3}} - \frac{36e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x^{3}} + \frac{144*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} + \frac{144e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x^{2}} + \frac{144e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x^{2}} + \frac{108*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{3}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos(3x)}{x^{2}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-sin(3x)*3}{x^{2}} + \frac{729*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{2x^{3}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos^{2}(3x)}{2x^{2}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-2cos(3x)sin(3x)*3}{2x^{2}} - \frac{432*-e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos(3x)}{x} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-sin(3x)*3}{x} + \frac{162*-e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} + \frac{162e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x} + \frac{162e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x} + 128e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)\\=&\frac{1458e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{4}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)cos(3x)}{8x^{5}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos^{2}(3x)}{8x^{4}} - \frac{2916e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{3}} - \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{3}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{2x^{2}} - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{5}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{3}(3x)}{8x^{6}} + \frac{486e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{4}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{4}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} - \frac{324e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{3}} + \frac{378e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} + \frac{1296e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} - \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{3}(3x)}{8x^{3}} + \frac{4374e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{2}} + \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{2x^{3}} - \frac{2106e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x} + \frac{1944e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x} + 512e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{1458e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{4}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)cos(3x)}{8x^{5}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos^{2}(3x)}{8x^{4}} - \frac{2916e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{3}} - \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{3}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{2x^{2}} - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{5}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{3}(3x)}{8x^{6}} + \frac{486e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{4}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{4}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} - \frac{324e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{3}} + \frac{378e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} + \frac{1296e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} - \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{3}(3x)}{8x^{3}} + \frac{4374e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{2}} + \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{2x^{3}} - \frac{2106e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x} + \frac{1944e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x} + 512e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\right)}{dx}\\=&\frac{1458*-4e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{5}} + \frac{1458e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)cos(3x)}{x^{4}} + \frac{1458e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3cos(3x)}{x^{4}} + \frac{1458e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)*-sin(3x)*3}{x^{4}} - \frac{6561*-5e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)cos(3x)}{8x^{6}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin^{2}(3x)cos(3x)}{8x^{5}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*2sin(3x)cos(3x)*3cos(3x)}{8x^{5}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)*-sin(3x)*3}{8x^{5}} + \frac{19683*-4e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos^{2}(3x)}{8x^{5}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)cos^{2}(3x)}{8x^{4}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3cos^{2}(3x)}{8x^{4}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)*-2cos(3x)sin(3x)*3}{8x^{4}} - \frac{2916*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{4}} - \frac{2916e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)cos(3x)}{x^{3}} - \frac{2916e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3cos(3x)}{x^{3}} - \frac{2916e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)*-sin(3x)*3}{x^{3}} - \frac{2187*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{4}} - \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos^{2}(3x)}{x^{3}} - \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-2cos(3x)sin(3x)*3}{x^{3}} - \frac{6561*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{2x^{3}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)cos(3x)}{2x^{2}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3cos(3x)}{2x^{2}} - \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)*-sin(3x)*3}{2x^{2}} - \frac{243*-5e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{6}} - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin^{2}(3x)}{x^{5}} - \frac{243e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*2sin(3x)cos(3x)*3}{x^{5}} + \frac{729*-6e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{3}(3x)}{8x^{7}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin^{3}(3x)}{8x^{6}} + \frac{729e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*3sin^{2}(3x)cos(3x)*3}{8x^{6}} + \frac{486*-4e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{5}} + \frac{486e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin^{2}(3x)}{x^{4}} + \frac{486e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*2sin(3x)cos(3x)*3}{x^{4}} + \frac{108*-4e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{5}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x^{4}} + \frac{108e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x^{4}} - \frac{432*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{4}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x^{3}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x^{3}} - \frac{324*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{4}} - \frac{324e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos(3x)}{x^{3}} - \frac{324e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-sin(3x)*3}{x^{3}} + \frac{378*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} + \frac{378e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x^{2}} + \frac{378e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x^{2}} + \frac{1296*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{3}} + \frac{1296e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos(3x)}{x^{2}} + \frac{1296e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-sin(3x)*3}{x^{2}} - \frac{19683*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{3}(3x)}{8x^{4}} - \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos^{3}(3x)}{8x^{3}} - \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-3cos^{2}(3x)sin(3x)*3}{8x^{3}} + \frac{4374*-2e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{3}} + \frac{4374e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos^{2}(3x)}{x^{2}} + \frac{4374e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-2cos(3x)sin(3x)*3}{x^{2}} + \frac{2187*-3e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{2x^{4}} + \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin^{2}(3x)}{2x^{3}} + \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*2sin(3x)cos(3x)*3}{2x^{3}} - \frac{2106*-e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} - \frac{2106e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)cos(3x)}{x} - \frac{2106e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}*-sin(3x)*3}{x} + \frac{1944*-e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} + \frac{1944e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)sin(3x)}{x} + \frac{1944e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)*3}{x} + 512e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}(\frac{\frac{-9}{4}*-sin(3x)}{x^{2}} - \frac{\frac{9}{4}cos(3x)*3}{x} + 4)\\=& - \frac{8748e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{5}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)cos(3x)}{2x^{6}} - \frac{59049e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos^{2}(3x)}{2x^{5}} + \frac{23328e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{4}} + \frac{13122e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{4}} - \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{3}(3x)cos(3x)}{8x^{7}} + \frac{177147e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)cos^{2}(3x)}{16x^{6}} - \frac{13122e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)cos(3x)}{x^{5}} - \frac{59049e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)cos(3x)}{2x^{4}} - \frac{177147e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos^{3}(3x)}{8x^{5}} + \frac{39366e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos^{2}(3x)}{x^{4}} + \frac{7290e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{3}} + \frac{59049e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{3}(3x)}{2x^{4}} + \frac{177147e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos^{2}(3x)}{4x^{3}} - \frac{52488e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)cos(3x)}{x^{2}} - \frac{34992e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{3}} + \frac{17496e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{3}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{3}(3x)}{4x^{5}} - \frac{4860e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{4}} + \frac{21870e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{2}(3x)}{x^{2}} + \frac{19683e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{2x^{2}} + \frac{1458e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{6}} - \frac{2187e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{3}(3x)}{2x^{7}} - \frac{3888e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{2}(3x)}{x^{5}} + \frac{6561e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{4}(3x)}{32x^{8}} + \frac{1458e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin^{3}(3x)}{x^{6}} - \frac{432e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{5}} + \frac{1728e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{4}} + \frac{1296e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{4}} - \frac{1512e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{3}} - \frac{5184e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{3}} - \frac{3168e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x^{2}} + \frac{8424e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x^{2}} + \frac{531441e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{4}(3x)}{32x^{4}} - \frac{39366e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos^{3}(3x)}{x^{3}} - \frac{6048e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}cos(3x)}{x} + \frac{14094e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}sin(3x)}{x} + 2048e^{\frac{\frac{-9}{4}sin(3x)}{x} + 4x}\\ \end{split}\end{equation} \]

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