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