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。
\[ \begin{equation}\begin{split}【1/1】求函数{sin(x)}^{e} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {sin(x)}^{e}\right)}{dx}\\=&({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))\\=&\frac{{sin(x)}^{e}ecos(x)}{sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{sin(x)}^{e}ecos(x)}{sin(x)}\right)}{dx}\\=&\frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos(x)}{sin(x)} + \frac{{sin(x)}^{e}*0cos(x)}{sin(x)} + \frac{{sin(x)}^{e}e*-cos(x)cos(x)}{sin^{2}(x)} + \frac{{sin(x)}^{e}e*-sin(x)}{sin(x)}\\=&\frac{{sin(x)}^{e}e^{2}cos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}ecos^{2}(x)}{sin^{2}(x)} - {sin(x)}^{e}e\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{sin(x)}^{e}e^{2}cos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}ecos^{2}(x)}{sin^{2}(x)} - {sin(x)}^{e}e\right)}{dx}\\=&\frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{2}cos^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{e}*2e*0cos^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{e}e^{2}*-2cos(x)cos^{2}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{e}e^{2}*-2cos(x)sin(x)}{sin^{2}(x)} - \frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}*0cos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}e*-2cos(x)cos^{2}(x)}{sin^{3}(x)} - \frac{{sin(x)}^{e}e*-2cos(x)sin(x)}{sin^{2}(x)} - ({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e - {sin(x)}^{e}*0\\=&\frac{{sin(x)}^{e}e^{3}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos(x)}{sin(x)} + \frac{2{sin(x)}^{e}ecos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}ecos(x)}{sin(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{{sin(x)}^{e}e^{3}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos(x)}{sin(x)} + \frac{2{sin(x)}^{e}ecos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}ecos(x)}{sin(x)}\right)}{dx}\\=&\frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{3}cos^{3}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{e}*3e^{2}*0cos^{3}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{e}e^{3}*-3cos(x)cos^{3}(x)}{sin^{4}(x)} + \frac{{sin(x)}^{e}e^{3}*-3cos^{2}(x)sin(x)}{sin^{3}(x)} - \frac{3({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{2}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}*2e*0cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}*-3cos(x)cos^{3}(x)}{sin^{4}(x)} - \frac{3{sin(x)}^{e}e^{2}*-3cos^{2}(x)sin(x)}{sin^{3}(x)} - \frac{3({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{2}cos(x)}{sin(x)} - \frac{3{sin(x)}^{e}*2e*0cos(x)}{sin(x)} - \frac{3{sin(x)}^{e}e^{2}*-cos(x)cos(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{e}e^{2}*-sin(x)}{sin(x)} + \frac{2({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}*0cos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}e*-3cos(x)cos^{3}(x)}{sin^{4}(x)} + \frac{2{sin(x)}^{e}e*-3cos^{2}(x)sin(x)}{sin^{3}(x)} + \frac{2({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos(x)}{sin(x)} + \frac{2{sin(x)}^{e}*0cos(x)}{sin(x)} + \frac{2{sin(x)}^{e}e*-cos(x)cos(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{e}e*-sin(x)}{sin(x)}\\=&\frac{{sin(x)}^{e}e^{4}cos^{4}(x)}{sin^{4}(x)} - \frac{6{sin(x)}^{e}e^{3}cos^{4}(x)}{sin^{4}(x)} - \frac{6{sin(x)}^{e}e^{3}cos^{2}(x)}{sin^{2}(x)} + \frac{11{sin(x)}^{e}e^{2}cos^{4}(x)}{sin^{4}(x)} + \frac{14{sin(x)}^{e}e^{2}cos^{2}(x)}{sin^{2}(x)} - \frac{6{sin(x)}^{e}ecos^{4}(x)}{sin^{4}(x)} - \frac{8{sin(x)}^{e}ecos^{2}(x)}{sin^{2}(x)} + 3{sin(x)}^{e}e^{2} - 2{sin(x)}^{e}e\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{sin(x)}^{e} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {sin(x)}^{e}\right)}{dx}\\=&({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))\\=&\frac{{sin(x)}^{e}ecos(x)}{sin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{sin(x)}^{e}ecos(x)}{sin(x)}\right)}{dx}\\=&\frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos(x)}{sin(x)} + \frac{{sin(x)}^{e}*0cos(x)}{sin(x)} + \frac{{sin(x)}^{e}e*-cos(x)cos(x)}{sin^{2}(x)} + \frac{{sin(x)}^{e}e*-sin(x)}{sin(x)}\\=&\frac{{sin(x)}^{e}e^{2}cos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}ecos^{2}(x)}{sin^{2}(x)} - {sin(x)}^{e}e\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{sin(x)}^{e}e^{2}cos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}ecos^{2}(x)}{sin^{2}(x)} - {sin(x)}^{e}e\right)}{dx}\\=&\frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{2}cos^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{e}*2e*0cos^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{e}e^{2}*-2cos(x)cos^{2}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{e}e^{2}*-2cos(x)sin(x)}{sin^{2}(x)} - \frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}*0cos^{2}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{e}e*-2cos(x)cos^{2}(x)}{sin^{3}(x)} - \frac{{sin(x)}^{e}e*-2cos(x)sin(x)}{sin^{2}(x)} - ({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e - {sin(x)}^{e}*0\\=&\frac{{sin(x)}^{e}e^{3}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos(x)}{sin(x)} + \frac{2{sin(x)}^{e}ecos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}ecos(x)}{sin(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{{sin(x)}^{e}e^{3}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}cos(x)}{sin(x)} + \frac{2{sin(x)}^{e}ecos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}ecos(x)}{sin(x)}\right)}{dx}\\=&\frac{({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{3}cos^{3}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{e}*3e^{2}*0cos^{3}(x)}{sin^{3}(x)} + \frac{{sin(x)}^{e}e^{3}*-3cos(x)cos^{3}(x)}{sin^{4}(x)} + \frac{{sin(x)}^{e}e^{3}*-3cos^{2}(x)sin(x)}{sin^{3}(x)} - \frac{3({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{2}cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}*2e*0cos^{3}(x)}{sin^{3}(x)} - \frac{3{sin(x)}^{e}e^{2}*-3cos(x)cos^{3}(x)}{sin^{4}(x)} - \frac{3{sin(x)}^{e}e^{2}*-3cos^{2}(x)sin(x)}{sin^{3}(x)} - \frac{3({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))e^{2}cos(x)}{sin(x)} - \frac{3{sin(x)}^{e}*2e*0cos(x)}{sin(x)} - \frac{3{sin(x)}^{e}e^{2}*-cos(x)cos(x)}{sin^{2}(x)} - \frac{3{sin(x)}^{e}e^{2}*-sin(x)}{sin(x)} + \frac{2({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}*0cos^{3}(x)}{sin^{3}(x)} + \frac{2{sin(x)}^{e}e*-3cos(x)cos^{3}(x)}{sin^{4}(x)} + \frac{2{sin(x)}^{e}e*-3cos^{2}(x)sin(x)}{sin^{3}(x)} + \frac{2({sin(x)}^{e}((0)ln(sin(x)) + \frac{(e)(cos(x))}{(sin(x))}))ecos(x)}{sin(x)} + \frac{2{sin(x)}^{e}*0cos(x)}{sin(x)} + \frac{2{sin(x)}^{e}e*-cos(x)cos(x)}{sin^{2}(x)} + \frac{2{sin(x)}^{e}e*-sin(x)}{sin(x)}\\=&\frac{{sin(x)}^{e}e^{4}cos^{4}(x)}{sin^{4}(x)} - \frac{6{sin(x)}^{e}e^{3}cos^{4}(x)}{sin^{4}(x)} - \frac{6{sin(x)}^{e}e^{3}cos^{2}(x)}{sin^{2}(x)} + \frac{11{sin(x)}^{e}e^{2}cos^{4}(x)}{sin^{4}(x)} + \frac{14{sin(x)}^{e}e^{2}cos^{2}(x)}{sin^{2}(x)} - \frac{6{sin(x)}^{e}ecos^{4}(x)}{sin^{4}(x)} - \frac{8{sin(x)}^{e}ecos^{2}(x)}{sin^{2}(x)} + 3{sin(x)}^{e}e^{2} - 2{sin(x)}^{e}e\\ \end{split}\end{equation} \]
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