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。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt({x}^{2}{sin(sqrt(sqrt(x)))}^{2}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(x^{2}sin^{2}(sqrt(sqrt(x))))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(x^{2}sin^{2}(sqrt(sqrt(x))))\right)}{dx}\\=&\frac{(2xsin^{2}(sqrt(sqrt(x))) + \frac{x^{2}*2sin(sqrt(sqrt(x)))cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}})*\frac{1}{2}}{(x^{2}sin^{2}(sqrt(sqrt(x))))^{\frac{1}{2}}}\\=&sin(sqrt(sqrt(x))) + \frac{x^{\frac{1}{2}}cos(sqrt(sqrt(x)))}{4sqrt(x)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sin(sqrt(sqrt(x))) + \frac{x^{\frac{1}{2}}cos(sqrt(sqrt(x)))}{4sqrt(x)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}} + \frac{\frac{1}{2}cos(sqrt(sqrt(x)))}{4x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{x^{\frac{1}{2}}*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{4(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{x^{\frac{1}{2}}cos(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{4(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}}\\=&\frac{3cos(sqrt(sqrt(x)))}{8x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{sin(sqrt(sqrt(x)))}{16sqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{16x^{\frac{3}{4}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{3cos(sqrt(sqrt(x)))}{8x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{sin(sqrt(sqrt(x)))}{16sqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{16x^{\frac{3}{4}}}\right)}{dx}\\=&\frac{3*\frac{-1}{2}cos(sqrt(sqrt(x)))}{8x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{3*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{8x^{\frac{1}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{3cos(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{8x^{\frac{1}{2}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} - \frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{16(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)} - \frac{sin(sqrt(sqrt(x)))*-\frac{1}{2}}{16(x)(x)^{\frac{1}{2}}} - \frac{\frac{-3}{4}cos(sqrt(sqrt(x)))}{16x^{\frac{7}{4}}} - \frac{-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{16x^{\frac{3}{4}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}}\\=&\frac{-3cos(sqrt(sqrt(x)))}{16x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3sin(sqrt(sqrt(x)))}{32xsqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{64x^{\frac{1}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{3cos(sqrt(sqrt(x)))}{64x^{\frac{7}{4}}} + \frac{sin(sqrt(sqrt(x)))}{64x^{\frac{5}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{sin(sqrt(sqrt(x)))}{32x^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3cos(sqrt(sqrt(x)))}{16x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3sin(sqrt(sqrt(x)))}{32xsqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{64x^{\frac{1}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{3cos(sqrt(sqrt(x)))}{64x^{\frac{7}{4}}} + \frac{sin(sqrt(sqrt(x)))}{64x^{\frac{5}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{sin(sqrt(sqrt(x)))}{32x^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-3*\frac{-3}{2}cos(sqrt(sqrt(x)))}{16x^{\frac{5}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{16x^{\frac{3}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3cos(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{16x^{\frac{3}{2}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} - \frac{3*-sin(sqrt(sqrt(x)))}{32x^{2}sqrt(x)} - \frac{3cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{32x(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)} - \frac{3sin(sqrt(sqrt(x)))*-\frac{1}{2}}{32x(x)(x)^{\frac{1}{2}}} - \frac{\frac{-1}{2}cos(sqrt(sqrt(x)))}{64x^{\frac{3}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{64x^{\frac{1}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{cos(sqrt(sqrt(x)))*\frac{-3}{2}*\frac{1}{2}}{64x^{\frac{1}{2}}(x)^{\frac{5}{4}}(x)^{\frac{1}{2}}} - \frac{3*\frac{-7}{4}cos(sqrt(sqrt(x)))}{64x^{\frac{11}{4}}} - \frac{3*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{64x^{\frac{7}{4}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}} + \frac{\frac{-5}{4}sin(sqrt(sqrt(x)))}{64x^{\frac{9}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{64x^{\frac{5}{4}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{sin(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{64x^{\frac{5}{4}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} + \frac{\frac{-3}{2}sin(sqrt(sqrt(x)))}{32x^{\frac{5}{2}}} + \frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{32x^{\frac{3}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}}\\=&\frac{9cos(sqrt(sqrt(x)))}{32x^{\frac{5}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{9sin(sqrt(sqrt(x)))}{64x^{2}sqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{64x^{\frac{3}{2}}sqrt(x)^{\frac{3}{2}}} + \frac{cos(sqrt(sqrt(x)))}{256x^{\frac{7}{4}}sqrt(x)} + \frac{sin(sqrt(sqrt(x)))}{256xsqrt(x)^{2}} - \frac{sin(sqrt(sqrt(x)))}{128x^{\frac{9}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{cos(sqrt(sqrt(x)))}{128x^{2}sqrt(x)^{\frac{1}{2}}} - \frac{sin(sqrt(sqrt(x)))}{256x^{\frac{5}{2}}} + \frac{33cos(sqrt(sqrt(x)))}{256x^{\frac{11}{4}}} + \frac{3cos(sqrt(sqrt(x)))}{256x^{\frac{9}{4}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt({x}^{2}{sin(sqrt(sqrt(x)))}^{2}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(x^{2}sin^{2}(sqrt(sqrt(x))))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(x^{2}sin^{2}(sqrt(sqrt(x))))\right)}{dx}\\=&\frac{(2xsin^{2}(sqrt(sqrt(x))) + \frac{x^{2}*2sin(sqrt(sqrt(x)))cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}})*\frac{1}{2}}{(x^{2}sin^{2}(sqrt(sqrt(x))))^{\frac{1}{2}}}\\=&sin(sqrt(sqrt(x))) + \frac{x^{\frac{1}{2}}cos(sqrt(sqrt(x)))}{4sqrt(x)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( sin(sqrt(sqrt(x))) + \frac{x^{\frac{1}{2}}cos(sqrt(sqrt(x)))}{4sqrt(x)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}} + \frac{\frac{1}{2}cos(sqrt(sqrt(x)))}{4x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{x^{\frac{1}{2}}*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{4(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{x^{\frac{1}{2}}cos(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{4(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}}\\=&\frac{3cos(sqrt(sqrt(x)))}{8x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{sin(sqrt(sqrt(x)))}{16sqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{16x^{\frac{3}{4}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{3cos(sqrt(sqrt(x)))}{8x^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{sin(sqrt(sqrt(x)))}{16sqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{16x^{\frac{3}{4}}}\right)}{dx}\\=&\frac{3*\frac{-1}{2}cos(sqrt(sqrt(x)))}{8x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{3*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{8x^{\frac{1}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{3cos(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{8x^{\frac{1}{2}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} - \frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{16(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)} - \frac{sin(sqrt(sqrt(x)))*-\frac{1}{2}}{16(x)(x)^{\frac{1}{2}}} - \frac{\frac{-3}{4}cos(sqrt(sqrt(x)))}{16x^{\frac{7}{4}}} - \frac{-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{16x^{\frac{3}{4}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}}\\=&\frac{-3cos(sqrt(sqrt(x)))}{16x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3sin(sqrt(sqrt(x)))}{32xsqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{64x^{\frac{1}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{3cos(sqrt(sqrt(x)))}{64x^{\frac{7}{4}}} + \frac{sin(sqrt(sqrt(x)))}{64x^{\frac{5}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{sin(sqrt(sqrt(x)))}{32x^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3cos(sqrt(sqrt(x)))}{16x^{\frac{3}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3sin(sqrt(sqrt(x)))}{32xsqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{64x^{\frac{1}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{3cos(sqrt(sqrt(x)))}{64x^{\frac{7}{4}}} + \frac{sin(sqrt(sqrt(x)))}{64x^{\frac{5}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{sin(sqrt(sqrt(x)))}{32x^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-3*\frac{-3}{2}cos(sqrt(sqrt(x)))}{16x^{\frac{5}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{16x^{\frac{3}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} - \frac{3cos(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{16x^{\frac{3}{2}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} - \frac{3*-sin(sqrt(sqrt(x)))}{32x^{2}sqrt(x)} - \frac{3cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{32x(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)} - \frac{3sin(sqrt(sqrt(x)))*-\frac{1}{2}}{32x(x)(x)^{\frac{1}{2}}} - \frac{\frac{-1}{2}cos(sqrt(sqrt(x)))}{64x^{\frac{3}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{64x^{\frac{1}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{3}{2}}} - \frac{cos(sqrt(sqrt(x)))*\frac{-3}{2}*\frac{1}{2}}{64x^{\frac{1}{2}}(x)^{\frac{5}{4}}(x)^{\frac{1}{2}}} - \frac{3*\frac{-7}{4}cos(sqrt(sqrt(x)))}{64x^{\frac{11}{4}}} - \frac{3*-sin(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{64x^{\frac{7}{4}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}} + \frac{\frac{-5}{4}sin(sqrt(sqrt(x)))}{64x^{\frac{9}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{64x^{\frac{5}{4}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{sin(sqrt(sqrt(x)))*\frac{-1}{2}*\frac{1}{2}}{64x^{\frac{5}{4}}(x)^{\frac{3}{4}}(x)^{\frac{1}{2}}} + \frac{\frac{-3}{2}sin(sqrt(sqrt(x)))}{32x^{\frac{5}{2}}} + \frac{cos(sqrt(sqrt(x)))*\frac{1}{2}*\frac{1}{2}}{32x^{\frac{3}{2}}(x)^{\frac{1}{2}}(sqrt(x))^{\frac{1}{2}}}\\=&\frac{9cos(sqrt(sqrt(x)))}{32x^{\frac{5}{2}}sqrt(x)^{\frac{1}{2}}} + \frac{9sin(sqrt(sqrt(x)))}{64x^{2}sqrt(x)} - \frac{cos(sqrt(sqrt(x)))}{64x^{\frac{3}{2}}sqrt(x)^{\frac{3}{2}}} + \frac{cos(sqrt(sqrt(x)))}{256x^{\frac{7}{4}}sqrt(x)} + \frac{sin(sqrt(sqrt(x)))}{256xsqrt(x)^{2}} - \frac{sin(sqrt(sqrt(x)))}{128x^{\frac{9}{4}}sqrt(x)^{\frac{1}{2}}} + \frac{cos(sqrt(sqrt(x)))}{128x^{2}sqrt(x)^{\frac{1}{2}}} - \frac{sin(sqrt(sqrt(x)))}{256x^{\frac{5}{2}}} + \frac{33cos(sqrt(sqrt(x)))}{256x^{\frac{11}{4}}} + \frac{3cos(sqrt(sqrt(x)))}{256x^{\frac{9}{4}}}\\ \end{split}\end{equation} \]
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