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。
\[ \begin{equation}\begin{split}【1/1】求函数2xarcsin(0.75x) + sin(5x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 2xarcsin(0.75x) + sin(5x)\right)}{dx}\\=&2arcsin(0.75x) + 2x(\frac{(0.75)}{((1 - (0.75x)^{2})^{\frac{1}{2}})}) + cos(5x)*5\\=&2arcsin(0.75x) + \frac{1.5x}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + 5cos(5x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2arcsin(0.75x) + \frac{1.5x}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + 5cos(5x)\right)}{dx}\\=&2(\frac{(0.75)}{((1 - (0.75x)^{2})^{\frac{1}{2}})}) + 1.5(\frac{-0.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{3}{2}}})x + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + 5*-sin(5x)*5\\=&\frac{0.84375x^{2}}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} - 25sin(5x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{0.84375x^{2}}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} - 25sin(5x)\right)}{dx}\\=&0.84375(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x^{2} + \frac{0.84375*2x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 1.5(\frac{-0.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{3}{2}}}) + 1.5(\frac{-0.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{3}{2}}}) - 25cos(5x)*5\\=&\frac{1.423828125x^{3}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.6875x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} - 125cos(5x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{1.423828125x^{3}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.6875x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} - 125cos(5x)\right)}{dx}\\=&1.423828125(\frac{-2.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{7}{2}}})x^{3} + \frac{1.423828125*3x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + 1.6875(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x + \frac{1.6875}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 0.84375(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 0.84375(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} - 125*-sin(5x)*5\\=&\frac{4.0045166015625x^{4}}{(-0.5625x^{2} + 1)^{\frac{7}{2}}} + \frac{2.84765625x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.423828125x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.423828125x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{4.271484375x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{1.6875}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 625sin(5x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数2xarcsin(0.75x) + sin(5x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 2xarcsin(0.75x) + sin(5x)\right)}{dx}\\=&2arcsin(0.75x) + 2x(\frac{(0.75)}{((1 - (0.75x)^{2})^{\frac{1}{2}})}) + cos(5x)*5\\=&2arcsin(0.75x) + \frac{1.5x}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + 5cos(5x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2arcsin(0.75x) + \frac{1.5x}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + 5cos(5x)\right)}{dx}\\=&2(\frac{(0.75)}{((1 - (0.75x)^{2})^{\frac{1}{2}})}) + 1.5(\frac{-0.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{3}{2}}})x + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + 5*-sin(5x)*5\\=&\frac{0.84375x^{2}}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} - 25sin(5x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{0.84375x^{2}}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} + \frac{1.5}{(-0.5625x^{2} + 1)^{\frac{1}{2}}} - 25sin(5x)\right)}{dx}\\=&0.84375(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x^{2} + \frac{0.84375*2x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 1.5(\frac{-0.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{3}{2}}}) + 1.5(\frac{-0.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{3}{2}}}) - 25cos(5x)*5\\=&\frac{1.423828125x^{3}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.6875x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} - 125cos(5x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{1.423828125x^{3}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.6875x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375x}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} - 125cos(5x)\right)}{dx}\\=&1.423828125(\frac{-2.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{7}{2}}})x^{3} + \frac{1.423828125*3x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + 1.6875(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x + \frac{1.6875}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 0.84375(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 0.84375(\frac{-1.5(-0.5625*2x + 0)}{(-0.5625x^{2} + 1)^{\frac{5}{2}}})x + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} - 125*-sin(5x)*5\\=&\frac{4.0045166015625x^{4}}{(-0.5625x^{2} + 1)^{\frac{7}{2}}} + \frac{2.84765625x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.423828125x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{1.423828125x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{4.271484375x^{2}}{(-0.5625x^{2} + 1)^{\frac{5}{2}}} + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{1.6875}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + \frac{0.84375}{(-0.5625x^{2} + 1)^{\frac{3}{2}}} + 625sin(5x)\\ \end{split}\end{equation} \]
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