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 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(3x)cos(0.75x){e}^{(2x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {e}^{(2x)}sin(3x)cos(0.75x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {e}^{(2x)}sin(3x)cos(0.75x)\right)}{dx}\\=&({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + {e}^{(2x)}cos(3x)*3cos(0.75x) - {e}^{(2x)}sin(3x)sin(0.75x)*0.75\\=&2{e}^{(2x)}sin(3x)cos(0.75x) + 3{e}^{(2x)}cos(3x)cos(0.75x) - 0.75{e}^{(2x)}sin(3x)sin(0.75x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2{e}^{(2x)}sin(3x)cos(0.75x) + 3{e}^{(2x)}cos(3x)cos(0.75x) - 0.75{e}^{(2x)}sin(3x)sin(0.75x)\right)}{dx}\\=&2({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + 2{e}^{(2x)}cos(3x)*3cos(0.75x) + 2{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 3{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 3{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 0.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 0.75{e}^{(2x)}cos(3x)*3sin(0.75x) - 0.75{e}^{(2x)}sin(3x)cos(0.75x)*0.75\\=&4{e}^{(2x)}sin(3x)cos(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 9{e}^{(2x)}sin(3x)cos(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 0.5625{e}^{(2x)}sin(3x)cos(0.75x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 4{e}^{(2x)}sin(3x)cos(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 9{e}^{(2x)}sin(3x)cos(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 0.5625{e}^{(2x)}sin(3x)cos(0.75x)\right)}{dx}\\=&4({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + 4{e}^{(2x)}cos(3x)*3cos(0.75x) + 4{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 6({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 6{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 6{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 1.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 1.5{e}^{(2x)}cos(3x)*3sin(0.75x) - 1.5{e}^{(2x)}sin(3x)cos(0.75x)*0.75 + 6({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 6{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 6{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 9({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 9{e}^{(2x)}cos(3x)*3cos(0.75x) - 9{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 2.25({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 2.25{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 2.25{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 1.5{e}^{(2x)}cos(3x)*3sin(0.75x) - 1.5{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 2.25({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 2.25{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 2.25{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 0.5625({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 0.5625{e}^{(2x)}cos(3x)*3cos(0.75x) - 0.5625{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75\\=&8{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 3{e}^{(2x)}sin(3x)sin(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 27{e}^{(2x)}cos(3x)cos(0.75x) + 6.75{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 1.6875{e}^{(2x)}cos(3x)cos(0.75x) + 0.421875{e}^{(2x)}sin(3x)sin(0.75x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 8{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 3{e}^{(2x)}sin(3x)sin(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 27{e}^{(2x)}cos(3x)cos(0.75x) + 6.75{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 1.6875{e}^{(2x)}cos(3x)cos(0.75x) + 0.421875{e}^{(2x)}sin(3x)sin(0.75x)\right)}{dx}\\=&8({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + 8{e}^{(2x)}cos(3x)*3cos(0.75x) + 8{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 12{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 12{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 3{e}^{(2x)}cos(3x)*3sin(0.75x) - 3{e}^{(2x)}sin(3x)cos(0.75x)*0.75 + 12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 12{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 12{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 18({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 18{e}^{(2x)}cos(3x)*3cos(0.75x) - 18{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 3{e}^{(2x)}cos(3x)*3sin(0.75x) - 3{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.125({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 1.125{e}^{(2x)}cos(3x)*3cos(0.75x) - 1.125{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 12{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 12{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 18({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 18{e}^{(2x)}cos(3x)*3cos(0.75x) - 18{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 18({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 18{e}^{(2x)}cos(3x)*3cos(0.75x) - 18{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 27({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) - 27{e}^{(2x)}*-sin(3x)*3cos(0.75x) - 27{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 + 6.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) + 6.75{e}^{(2x)}cos(3x)*3sin(0.75x) + 6.75{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.6875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(0.75x)cos(3x) - 1.6875{e}^{(2x)}*-sin(0.75x)*0.75cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)*-sin(3x)*3 + 6.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)sin(3x) + 6.75{e}^{(2x)}cos(0.75x)*0.75sin(3x) + 6.75{e}^{(2x)}sin(0.75x)cos(3x)*3 - 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 3{e}^{(2x)}cos(3x)*3sin(0.75x) - 3{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.125({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 1.125{e}^{(2x)}cos(3x)*3cos(0.75x) - 1.125{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.6875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(0.75x)cos(3x) - 1.6875{e}^{(2x)}*-sin(0.75x)*0.75cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)*-sin(3x)*3 + 6.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)sin(3x) + 6.75{e}^{(2x)}cos(0.75x)*0.75sin(3x) + 6.75{e}^{(2x)}sin(0.75x)cos(3x)*3 - 1.125({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 1.125{e}^{(2x)}cos(3x)*3cos(0.75x) - 1.125{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 1.6875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) - 1.6875{e}^{(2x)}*-sin(3x)*3cos(0.75x) - 1.6875{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 + 0.421875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) + 0.421875{e}^{(2x)}cos(3x)*3sin(0.75x) + 0.421875{e}^{(2x)}sin(3x)cos(0.75x)*0.75\\=&16{e}^{(2x)}sin(3x)cos(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 6{e}^{(2x)}sin(3x)sin(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 6{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 6{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 81{e}^{(2x)}sin(3x)cos(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) - 6{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 0.31640625{e}^{(2x)}sin(3x)cos(0.75x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(3x)cos(0.75x){e}^{(2x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {e}^{(2x)}sin(3x)cos(0.75x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {e}^{(2x)}sin(3x)cos(0.75x)\right)}{dx}\\=&({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + {e}^{(2x)}cos(3x)*3cos(0.75x) - {e}^{(2x)}sin(3x)sin(0.75x)*0.75\\=&2{e}^{(2x)}sin(3x)cos(0.75x) + 3{e}^{(2x)}cos(3x)cos(0.75x) - 0.75{e}^{(2x)}sin(3x)sin(0.75x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2{e}^{(2x)}sin(3x)cos(0.75x) + 3{e}^{(2x)}cos(3x)cos(0.75x) - 0.75{e}^{(2x)}sin(3x)sin(0.75x)\right)}{dx}\\=&2({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + 2{e}^{(2x)}cos(3x)*3cos(0.75x) + 2{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 3{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 3{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 0.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 0.75{e}^{(2x)}cos(3x)*3sin(0.75x) - 0.75{e}^{(2x)}sin(3x)cos(0.75x)*0.75\\=&4{e}^{(2x)}sin(3x)cos(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 9{e}^{(2x)}sin(3x)cos(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 0.5625{e}^{(2x)}sin(3x)cos(0.75x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 4{e}^{(2x)}sin(3x)cos(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) + 6{e}^{(2x)}cos(3x)cos(0.75x) - 9{e}^{(2x)}sin(3x)cos(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 1.5{e}^{(2x)}sin(3x)sin(0.75x) - 2.25{e}^{(2x)}sin(0.75x)cos(3x) - 0.5625{e}^{(2x)}sin(3x)cos(0.75x)\right)}{dx}\\=&4({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + 4{e}^{(2x)}cos(3x)*3cos(0.75x) + 4{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 6({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 6{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 6{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 1.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 1.5{e}^{(2x)}cos(3x)*3sin(0.75x) - 1.5{e}^{(2x)}sin(3x)cos(0.75x)*0.75 + 6({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 6{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 6{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 9({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 9{e}^{(2x)}cos(3x)*3cos(0.75x) - 9{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 2.25({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 2.25{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 2.25{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 1.5{e}^{(2x)}cos(3x)*3sin(0.75x) - 1.5{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 2.25({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 2.25{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 2.25{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 0.5625({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 0.5625{e}^{(2x)}cos(3x)*3cos(0.75x) - 0.5625{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75\\=&8{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 3{e}^{(2x)}sin(3x)sin(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 27{e}^{(2x)}cos(3x)cos(0.75x) + 6.75{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 1.6875{e}^{(2x)}cos(3x)cos(0.75x) + 0.421875{e}^{(2x)}sin(3x)sin(0.75x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 8{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 3{e}^{(2x)}sin(3x)sin(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) + 12{e}^{(2x)}cos(3x)cos(0.75x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 18{e}^{(2x)}sin(3x)cos(0.75x) - 27{e}^{(2x)}cos(3x)cos(0.75x) + 6.75{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 3{e}^{(2x)}sin(3x)sin(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 4.5{e}^{(2x)}sin(0.75x)cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)cos(3x) + 6.75{e}^{(2x)}sin(0.75x)sin(3x) - 1.125{e}^{(2x)}sin(3x)cos(0.75x) - 1.6875{e}^{(2x)}cos(3x)cos(0.75x) + 0.421875{e}^{(2x)}sin(3x)sin(0.75x)\right)}{dx}\\=&8({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) + 8{e}^{(2x)}cos(3x)*3cos(0.75x) + 8{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 12{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 12{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 3{e}^{(2x)}cos(3x)*3sin(0.75x) - 3{e}^{(2x)}sin(3x)cos(0.75x)*0.75 + 12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 12{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 12{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 18({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 18{e}^{(2x)}cos(3x)*3cos(0.75x) - 18{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 3{e}^{(2x)}cos(3x)*3sin(0.75x) - 3{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.125({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 1.125{e}^{(2x)}cos(3x)*3cos(0.75x) - 1.125{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 + 12({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) + 12{e}^{(2x)}*-sin(3x)*3cos(0.75x) + 12{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 - 18({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 18{e}^{(2x)}cos(3x)*3cos(0.75x) - 18{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 18({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 18{e}^{(2x)}cos(3x)*3cos(0.75x) - 18{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 27({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) - 27{e}^{(2x)}*-sin(3x)*3cos(0.75x) - 27{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 + 6.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) + 6.75{e}^{(2x)}cos(3x)*3sin(0.75x) + 6.75{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.6875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(0.75x)cos(3x) - 1.6875{e}^{(2x)}*-sin(0.75x)*0.75cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)*-sin(3x)*3 + 6.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)sin(3x) + 6.75{e}^{(2x)}cos(0.75x)*0.75sin(3x) + 6.75{e}^{(2x)}sin(0.75x)cos(3x)*3 - 3({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) - 3{e}^{(2x)}cos(3x)*3sin(0.75x) - 3{e}^{(2x)}sin(3x)cos(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.125({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 1.125{e}^{(2x)}cos(3x)*3cos(0.75x) - 1.125{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 4.5({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)cos(3x) - 4.5{e}^{(2x)}cos(0.75x)*0.75cos(3x) - 4.5{e}^{(2x)}sin(0.75x)*-sin(3x)*3 - 1.6875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(0.75x)cos(3x) - 1.6875{e}^{(2x)}*-sin(0.75x)*0.75cos(3x) - 1.6875{e}^{(2x)}cos(0.75x)*-sin(3x)*3 + 6.75({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(0.75x)sin(3x) + 6.75{e}^{(2x)}cos(0.75x)*0.75sin(3x) + 6.75{e}^{(2x)}sin(0.75x)cos(3x)*3 - 1.125({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)cos(0.75x) - 1.125{e}^{(2x)}cos(3x)*3cos(0.75x) - 1.125{e}^{(2x)}sin(3x)*-sin(0.75x)*0.75 - 1.6875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))cos(3x)cos(0.75x) - 1.6875{e}^{(2x)}*-sin(3x)*3cos(0.75x) - 1.6875{e}^{(2x)}cos(3x)*-sin(0.75x)*0.75 + 0.421875({e}^{(2x)}((2)ln(e) + \frac{(2x)(0)}{(e)}))sin(3x)sin(0.75x) + 0.421875{e}^{(2x)}cos(3x)*3sin(0.75x) + 0.421875{e}^{(2x)}sin(3x)cos(0.75x)*0.75\\=&16{e}^{(2x)}sin(3x)cos(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 6{e}^{(2x)}sin(3x)sin(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 6{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 6{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) + 24{e}^{(2x)}cos(3x)cos(0.75x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 36{e}^{(2x)}sin(3x)cos(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) - 54{e}^{(2x)}cos(3x)cos(0.75x) + 81{e}^{(2x)}sin(3x)cos(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(3x)sin(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) - 6{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) - 9{e}^{(2x)}sin(0.75x)cos(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) - 3.375{e}^{(2x)}cos(0.75x)cos(3x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 13.5{e}^{(2x)}sin(0.75x)sin(3x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 20.25{e}^{(2x)}sin(0.75x)cos(3x) - 2.25{e}^{(2x)}sin(3x)cos(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) - 3.375{e}^{(2x)}cos(3x)cos(0.75x) + 5.0625{e}^{(2x)}sin(3x)cos(0.75x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 0.84375{e}^{(2x)}sin(3x)sin(0.75x) + 1.265625{e}^{(2x)}sin(0.75x)cos(3x) + 0.31640625{e}^{(2x)}sin(3x)cos(0.75x)\\ \end{split}\end{equation} \]
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