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。
    当前位置:求导函数 > 导函数计算历史 > 答案

    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。
\[ \begin{equation}\begin{split}【1/1】求函数{(sin(x))}^{sh(x)} 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {sin(x)}^{sh(x)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( {sin(x)}^{sh(x)}\right)}{dx}\\=&({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))\\=&{sin(x)}^{sh(x)}ln(sin(x))ch(x) + \frac{{sin(x)}^{sh(x)}cos(x)sh(x)}{sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( {sin(x)}^{sh(x)}ln(sin(x))ch(x) + \frac{{sin(x)}^{sh(x)}cos(x)sh(x)}{sin(x)}\right)}{dx}\\=&({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))ch(x) + \frac{{sin(x)}^{sh(x)}cos(x)ch(x)}{(sin(x))} + {sin(x)}^{sh(x)}ln(sin(x))sh(x) + \frac{({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos(x)sh(x)}{sin(x)} + \frac{{sin(x)}^{sh(x)}*-cos(x)cos(x)sh(x)}{sin^{2}(x)} + \frac{{sin(x)}^{sh(x)}*-sin(x)sh(x)}{sin(x)} + \frac{{sin(x)}^{sh(x)}cos(x)ch(x)}{sin(x)}\\=&{sin(x)}^{sh(x)}ln^{2}(sin(x))ch^{2}(x) + \frac{2{sin(x)}^{sh(x)}ln(sin(x))cos(x)sh(x)ch(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}cos(x)ch(x)}{sin(x)} + {sin(x)}^{sh(x)}ln(sin(x))sh(x) + \frac{{sin(x)}^{sh(x)}cos^{2}(x)sh^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{sh(x)}cos^{2}(x)sh(x)}{sin^{2}(x)} - {sin(x)}^{sh(x)}sh(x)\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( {sin(x)}^{sh(x)}ln^{2}(sin(x))ch^{2}(x) + \frac{2{sin(x)}^{sh(x)}ln(sin(x))cos(x)sh(x)ch(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}cos(x)ch(x)}{sin(x)} + {sin(x)}^{sh(x)}ln(sin(x))sh(x) + \frac{{sin(x)}^{sh(x)}cos^{2}(x)sh^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{sh(x)}cos^{2}(x)sh(x)}{sin^{2}(x)} - {sin(x)}^{sh(x)}sh(x)\right)}{dx}\\=&({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln^{2}(sin(x))ch^{2}(x) + \frac{{sin(x)}^{sh(x)}*2ln(sin(x))cos(x)ch^{2}(x)}{(sin(x))} + {sin(x)}^{sh(x)}ln^{2}(sin(x))*2ch(x)sh(x) + \frac{2({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))cos(x)sh(x)ch(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}cos(x)cos(x)sh(x)ch(x)}{(sin(x))sin(x)} + \frac{2{sin(x)}^{sh(x)}ln(sin(x))*-cos(x)cos(x)sh(x)ch(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{sh(x)}ln(sin(x))*-sin(x)sh(x)ch(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}ln(sin(x))cos(x)ch(x)ch(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}ln(sin(x))cos(x)sh(x)sh(x)}{sin(x)} + \frac{2({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos(x)ch(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}*-cos(x)cos(x)ch(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{sh(x)}*-sin(x)ch(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}cos(x)sh(x)}{sin(x)} + ({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))sh(x) + \frac{{sin(x)}^{sh(x)}cos(x)sh(x)}{(sin(x))} + {sin(x)}^{sh(x)}ln(sin(x))ch(x) + \frac{({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos^{2}(x)sh^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{sh(x)}*-2cos(x)cos^{2}(x)sh^{2}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{sh(x)}*-2cos(x)sin(x)sh^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{sh(x)}cos^{2}(x)*2sh(x)ch(x)}{sin^{2}(x)} - \frac{({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos^{2}(x)sh(x)}{sin^{2}(x)} - \frac{{sin(x)}^{sh(x)}*-2cos(x)cos^{2}(x)sh(x)}{sin^{3}(x)} - \frac{{sin(x)}^{sh(x)}*-2cos(x)sin(x)sh(x)}{sin^{2}(x)} - \frac{{sin(x)}^{sh(x)}cos^{2}(x)ch(x)}{sin^{2}(x)} - ({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))sh(x) - {sin(x)}^{sh(x)}ch(x)\\=&{sin(x)}^{sh(x)}ln^{3}(sin(x))ch^{3}(x) + \frac{3{sin(x)}^{sh(x)}ln^{2}(sin(x))cos(x)sh(x)ch^{2}(x)}{sin(x)} + \frac{6{sin(x)}^{sh(x)}ln(sin(x))cos(x)ch^{2}(x)}{sin(x)} + 3{sin(x)}^{sh(x)}ln^{2}(sin(x))sh(x)ch(x) + \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh^{2}(x)ch(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{sh(x)}cos^{2}(x)sh(x)ch(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh(x)ch(x)}{sin^{2}(x)} - 3{sin(x)}^{sh(x)}ln(sin(x))sh(x)ch(x) + \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos(x)sh^{2}(x)}{sin(x)} - \frac{3{sin(x)}^{sh(x)}cos^{2}(x)ch(x)}{sin^{2}(x)} - 3{sin(x)}^{sh(x)}ch(x) + \frac{5{sin(x)}^{sh(x)}cos(x)sh(x)}{sin(x)} + {sin(x)}^{sh(x)}ln(sin(x))ch(x) + \frac{{sin(x)}^{sh(x)}cos^{3}(x)sh^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}cos^{3}(x)sh^{2}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}cos(x)sh^{2}(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}cos^{3}(x)sh(x)}{sin^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( {sin(x)}^{sh(x)}ln^{3}(sin(x))ch^{3}(x) + \frac{3{sin(x)}^{sh(x)}ln^{2}(sin(x))cos(x)sh(x)ch^{2}(x)}{sin(x)} + \frac{6{sin(x)}^{sh(x)}ln(sin(x))cos(x)ch^{2}(x)}{sin(x)} + 3{sin(x)}^{sh(x)}ln^{2}(sin(x))sh(x)ch(x) + \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh^{2}(x)ch(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{sh(x)}cos^{2}(x)sh(x)ch(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh(x)ch(x)}{sin^{2}(x)} - 3{sin(x)}^{sh(x)}ln(sin(x))sh(x)ch(x) + \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos(x)sh^{2}(x)}{sin(x)} - \frac{3{sin(x)}^{sh(x)}cos^{2}(x)ch(x)}{sin^{2}(x)} - 3{sin(x)}^{sh(x)}ch(x) + \frac{5{sin(x)}^{sh(x)}cos(x)sh(x)}{sin(x)} + {sin(x)}^{sh(x)}ln(sin(x))ch(x) + \frac{{sin(x)}^{sh(x)}cos^{3}(x)sh^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}cos^{3}(x)sh^{2}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}cos(x)sh^{2}(x)}{sin(x)} + \frac{2{sin(x)}^{sh(x)}cos^{3}(x)sh(x)}{sin^{3}(x)}\right)}{dx}\\=&({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln^{3}(sin(x))ch^{3}(x) + \frac{{sin(x)}^{sh(x)}*3ln^{2}(sin(x))cos(x)ch^{3}(x)}{(sin(x))} + {sin(x)}^{sh(x)}ln^{3}(sin(x))*3ch^{2}(x)sh(x) + \frac{3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln^{2}(sin(x))cos(x)sh(x)ch^{2}(x)}{sin(x)} + \frac{3{sin(x)}^{sh(x)}*2ln(sin(x))cos(x)cos(x)sh(x)ch^{2}(x)}{(sin(x))sin(x)} + \frac{3{sin(x)}^{sh(x)}ln^{2}(sin(x))*-cos(x)cos(x)sh(x)ch^{2}(x)}{sin^{2}(x)} + \frac{3{sin(x)}^{sh(x)}ln^{2}(sin(x))*-sin(x)sh(x)ch^{2}(x)}{sin(x)} + \frac{3{sin(x)}^{sh(x)}ln^{2}(sin(x))cos(x)ch(x)ch^{2}(x)}{sin(x)} + \frac{3{sin(x)}^{sh(x)}ln^{2}(sin(x))cos(x)sh(x)*2ch(x)sh(x)}{sin(x)} + \frac{6({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))cos(x)ch^{2}(x)}{sin(x)} + \frac{6{sin(x)}^{sh(x)}cos(x)cos(x)ch^{2}(x)}{(sin(x))sin(x)} + \frac{6{sin(x)}^{sh(x)}ln(sin(x))*-cos(x)cos(x)ch^{2}(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{sh(x)}ln(sin(x))*-sin(x)ch^{2}(x)}{sin(x)} + \frac{6{sin(x)}^{sh(x)}ln(sin(x))cos(x)*2ch(x)sh(x)}{sin(x)} + 3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln^{2}(sin(x))sh(x)ch(x) + \frac{3{sin(x)}^{sh(x)}*2ln(sin(x))cos(x)sh(x)ch(x)}{(sin(x))} + 3{sin(x)}^{sh(x)}ln^{2}(sin(x))ch(x)ch(x) + 3{sin(x)}^{sh(x)}ln^{2}(sin(x))sh(x)sh(x) + \frac{3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))cos^{2}(x)sh^{2}(x)ch(x)}{sin^{2}(x)} + \frac{3{sin(x)}^{sh(x)}cos(x)cos^{2}(x)sh^{2}(x)ch(x)}{(sin(x))sin^{2}(x)} + \frac{3{sin(x)}^{sh(x)}ln(sin(x))*-2cos(x)cos^{2}(x)sh^{2}(x)ch(x)}{sin^{3}(x)} + \frac{3{sin(x)}^{sh(x)}ln(sin(x))*-2cos(x)sin(x)sh^{2}(x)ch(x)}{sin^{2}(x)} + \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)*2sh(x)ch(x)ch(x)}{sin^{2}(x)} + \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh^{2}(x)sh(x)}{sin^{2}(x)} + \frac{6({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos^{2}(x)sh(x)ch(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{sh(x)}*-2cos(x)cos^{2}(x)sh(x)ch(x)}{sin^{3}(x)} + \frac{6{sin(x)}^{sh(x)}*-2cos(x)sin(x)sh(x)ch(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{sh(x)}cos^{2}(x)ch(x)ch(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{sh(x)}cos^{2}(x)sh(x)sh(x)}{sin^{2}(x)} - \frac{3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))cos^{2}(x)sh(x)ch(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}cos(x)cos^{2}(x)sh(x)ch(x)}{(sin(x))sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}ln(sin(x))*-2cos(x)cos^{2}(x)sh(x)ch(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}ln(sin(x))*-2cos(x)sin(x)sh(x)ch(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)ch(x)ch(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh(x)sh(x)}{sin^{2}(x)} - 3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))sh(x)ch(x) - \frac{3{sin(x)}^{sh(x)}cos(x)sh(x)ch(x)}{(sin(x))} - 3{sin(x)}^{sh(x)}ln(sin(x))ch(x)ch(x) - 3{sin(x)}^{sh(x)}ln(sin(x))sh(x)sh(x) + \frac{3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))cos(x)sh^{2}(x)}{sin(x)} + \frac{3{sin(x)}^{sh(x)}cos(x)cos(x)sh^{2}(x)}{(sin(x))sin(x)} + \frac{3{sin(x)}^{sh(x)}ln(sin(x))*-cos(x)cos(x)sh^{2}(x)}{sin^{2}(x)} + \frac{3{sin(x)}^{sh(x)}ln(sin(x))*-sin(x)sh^{2}(x)}{sin(x)} + \frac{3{sin(x)}^{sh(x)}ln(sin(x))cos(x)*2sh(x)ch(x)}{sin(x)} - \frac{3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos^{2}(x)ch(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}*-2cos(x)cos^{2}(x)ch(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}*-2cos(x)sin(x)ch(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}cos^{2}(x)sh(x)}{sin^{2}(x)} - 3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ch(x) - 3{sin(x)}^{sh(x)}sh(x) + \frac{5({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos(x)sh(x)}{sin(x)} + \frac{5{sin(x)}^{sh(x)}*-cos(x)cos(x)sh(x)}{sin^{2}(x)} + \frac{5{sin(x)}^{sh(x)}*-sin(x)sh(x)}{sin(x)} + \frac{5{sin(x)}^{sh(x)}cos(x)ch(x)}{sin(x)} + ({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))ln(sin(x))ch(x) + \frac{{sin(x)}^{sh(x)}cos(x)ch(x)}{(sin(x))} + {sin(x)}^{sh(x)}ln(sin(x))sh(x) + \frac{({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos^{3}(x)sh^{3}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{sh(x)}*-3cos(x)cos^{3}(x)sh^{3}(x)}{sin^{4}(x)} + \frac{{sin(x)}^{sh(x)}*-3cos^{2}(x)sin(x)sh^{3}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{sh(x)}cos^{3}(x)*3sh^{2}(x)ch(x)}{sin^{3}(x)} - \frac{3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos^{3}(x)sh^{2}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}*-3cos(x)cos^{3}(x)sh^{2}(x)}{sin^{4}(x)} - \frac{3{sin(x)}^{sh(x)}*-3cos^{2}(x)sin(x)sh^{2}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{sh(x)}cos^{3}(x)*2sh(x)ch(x)}{sin^{3}(x)} - \frac{3({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos(x)sh^{2}(x)}{sin(x)} - \frac{3{sin(x)}^{sh(x)}*-cos(x)cos(x)sh^{2}(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{sh(x)}*-sin(x)sh^{2}(x)}{sin(x)} - \frac{3{sin(x)}^{sh(x)}cos(x)*2sh(x)ch(x)}{sin(x)} + \frac{2({sin(x)}^{sh(x)}((ch(x))ln(sin(x)) + \frac{(sh(x))(cos(x))}{(sin(x))}))cos^{3}(x)sh(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{sh(x)}*-3cos(x)cos^{3}(x)sh(x)}{sin^{4}(x)} + \frac{2{sin(x)}^{sh(x)}*-3cos^{2}(x)sin(x)sh(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{sh(x)}cos^{3}(x)ch(x)}{sin^{3}(x)}\\=&{sin(x)}^{sh(x)}ln^{4}(sin(x))ch^{4}(x) + \frac{24{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh(x)ch^{2}(x)}{sin^{2}(x)} + \frac{12{sin(x)}^{sh(x)}ln^{2}(sin(x))cos(x)ch^{3}(x)}{sin(x)} + 6{sin(x)}^{sh(x)}ln^{3}(sin(x))sh(x)ch^{2}(x) + \frac{4{sin(x)}^{sh(x)}ln^{3}(sin(x))cos(x)sh(x)ch^{3}(x)}{sin(x)} + \frac{6{sin(x)}^{sh(x)}ln^{2}(sin(x))cos^{2}(x)sh^{2}(x)ch^{2}(x)}{sin^{2}(x)} - \frac{6{sin(x)}^{sh(x)}ln^{2}(sin(x))cos^{2}(x)sh(x)ch^{2}(x)}{sin^{2}(x)} - 6{sin(x)}^{sh(x)}ln^{2}(sin(x))sh(x)ch^{2}(x) + \frac{12{sin(x)}^{sh(x)}ln^{2}(sin(x))cos(x)sh^{2}(x)ch(x)}{sin(x)} + \frac{12{sin(x)}^{sh(x)}cos^{2}(x)ch^{2}(x)}{sin^{2}(x)} - \frac{12{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)ch^{2}(x)}{sin^{2}(x)} - 12{sin(x)}^{sh(x)}ln(sin(x))ch^{2}(x) + \frac{36{sin(x)}^{sh(x)}ln(sin(x))cos(x)sh(x)ch(x)}{sin(x)} + 4{sin(x)}^{sh(x)}ln^{2}(sin(x))ch^{2}(x) + 3{sin(x)}^{sh(x)}ln^{2}(sin(x))sh^{2}(x) + \frac{4{sin(x)}^{sh(x)}ln(sin(x))cos^{3}(x)sh^{3}(x)ch(x)}{sin^{3}(x)} + \frac{12{sin(x)}^{sh(x)}cos^{3}(x)sh^{2}(x)ch(x)}{sin^{3}(x)} - \frac{12{sin(x)}^{sh(x)}ln(sin(x))cos^{3}(x)sh^{2}(x)ch(x)}{sin^{3}(x)} - \frac{12{sin(x)}^{sh(x)}ln(sin(x))cos(x)sh^{2}(x)ch(x)}{sin(x)} + \frac{8{sin(x)}^{sh(x)}ln(sin(x))cos^{3}(x)sh(x)ch(x)}{sin^{3}(x)} - \frac{24{sin(x)}^{sh(x)}cos^{3}(x)sh(x)ch(x)}{sin^{3}(x)} - \frac{24{sin(x)}^{sh(x)}cos(x)sh(x)ch(x)}{sin(x)} + \frac{26{sin(x)}^{sh(x)}cos^{2}(x)sh^{2}(x)}{sin^{2}(x)} + \frac{6{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh^{3}(x)}{sin^{2}(x)} - \frac{6{sin(x)}^{sh(x)}ln(sin(x))cos^{2}(x)sh^{2}(x)}{sin^{2}(x)} - 6{sin(x)}^{sh(x)}ln(sin(x))sh^{2}(x) + \frac{8{sin(x)}^{sh(x)}cos^{3}(x)ch(x)}{sin^{3}(x)} + \frac{12{sin(x)}^{sh(x)}cos(x)ch(x)}{sin(x)} - 8{sin(x)}^{sh(x)}sh(x) - \frac{14{sin(x)}^{sh(x)}cos^{2}(x)sh(x)}{sin^{2}(x)} + {sin(x)}^{sh(x)}ln(sin(x))sh(x) + \frac{{sin(x)}^{sh(x)}cos^{4}(x)sh^{4}(x)}{sin^{4}(x)} - \frac{6{sin(x)}^{sh(x)}cos^{4}(x)sh^{3}(x)}{sin^{4}(x)} - \frac{6{sin(x)}^{sh(x)}cos^{2}(x)sh^{3}(x)}{sin^{2}(x)} + \frac{11{sin(x)}^{sh(x)}cos^{4}(x)sh^{2}(x)}{sin^{4}(x)} + 3{sin(x)}^{sh(x)}sh^{2}(x) - \frac{6{sin(x)}^{sh(x)}cos^{4}(x)sh(x)}{sin^{4}(x)}\\ \end{split}\end{equation} \]



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