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。
\[ \begin{equation}\begin{split}【1/1】求函数Aarcsin(wx + r) + B 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( Aarcsin(wx + r) + B\right)}{dx}\\=&A(\frac{(w + 0)}{((1 - (wx + r)^{2})^{\frac{1}{2}})}) + 0\\=&\frac{Aw}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{Aw}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}})Aw + 0\\=&\frac{Aw^{3}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + \frac{Aw^{2}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{Aw^{3}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + \frac{Aw^{2}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{3}x + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + (\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{2}r + 0\\=&\frac{3Aw^{5}x^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{6Aw^{4}rx}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{3Aw^{3}r^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3Aw^{5}x^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{6Aw^{4}rx}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{3Aw^{3}r^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{5}x^{2} + \frac{3Aw^{5}*2x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + 6(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{4}rx + \frac{6Aw^{4}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + 3(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{3}r^{2} + 0 + (\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{3} + 0\\=&\frac{15Aw^{7}x^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{45Aw^{6}rx^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{9Aw^{5}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{45Aw^{5}r^{2}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{9Aw^{4}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{15Aw^{4}r^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数Aarcsin(wx + r) + B 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( Aarcsin(wx + r) + B\right)}{dx}\\=&A(\frac{(w + 0)}{((1 - (wx + r)^{2})^{\frac{1}{2}})}) + 0\\=&\frac{Aw}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{Aw}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}})Aw + 0\\=&\frac{Aw^{3}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + \frac{Aw^{2}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{Aw^{3}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + \frac{Aw^{2}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{3}x + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + (\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{2}r + 0\\=&\frac{3Aw^{5}x^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{6Aw^{4}rx}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{3Aw^{3}r^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3Aw^{5}x^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{6Aw^{4}rx}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{3Aw^{3}r^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{5}x^{2} + \frac{3Aw^{5}*2x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + 6(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{4}rx + \frac{6Aw^{4}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + 3(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{3}r^{2} + 0 + (\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{3} + 0\\=&\frac{15Aw^{7}x^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{45Aw^{6}rx^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{9Aw^{5}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{45Aw^{5}r^{2}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{9Aw^{4}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{15Aw^{4}r^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]
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