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 3 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{3}^{(sin(\frac{(3{x}^{2})}{50}) + cos(x))} 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}\right)}{dx}\\=&({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))\\=&\frac{3x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(\frac{3}{50}x^{2})}{25} - {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)sin(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{3x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(\frac{3}{50}x^{2})}{25} - {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)sin(x)\right)}{dx}\\=&\frac{3 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(\frac{3}{50}x^{2})}{25} + \frac{3x({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln(3)cos(\frac{3}{50}x^{2})}{25} + \frac{3x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*0cos(\frac{3}{50}x^{2})}{25(3)} + \frac{3x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)*-sin(\frac{3}{50}x^{2})*\frac{3}{50}*2x}{25} - ({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln(3)sin(x) - \frac{{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*0sin(x)}{(3)} - {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(x)\\=&\frac{3 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(\frac{3}{50}x^{2})}{25} + \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)cos^{2}(\frac{3}{50}x^{2})}{625} - \frac{6x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(x)cos(\frac{3}{50}x^{2})}{25} - \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)sin(\frac{3}{50}x^{2})}{625} + {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin^{2}(x) - {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{3 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(\frac{3}{50}x^{2})}{25} + \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)cos^{2}(\frac{3}{50}x^{2})}{625} - \frac{6x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(x)cos(\frac{3}{50}x^{2})}{25} - \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)sin(\frac{3}{50}x^{2})}{625} + {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin^{2}(x) - {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(x)\right)}{dx}\\=&\frac{3({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln(3)cos(\frac{3}{50}x^{2})}{25} + \frac{3 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*0cos(\frac{3}{50}x^{2})}{25(3)} + \frac{3 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)*-sin(\frac{3}{50}x^{2})*\frac{3}{50}*2x}{25} + \frac{9*2x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)cos^{2}(\frac{3}{50}x^{2})}{625} + \frac{9x^{2}({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln^{2}(3)cos^{2}(\frac{3}{50}x^{2})}{625} + \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*2ln(3)*0cos^{2}(\frac{3}{50}x^{2})}{625(3)} + \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)*-2cos(\frac{3}{50}x^{2})sin(\frac{3}{50}x^{2})*\frac{3}{50}*2x}{625} - \frac{6 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(x)cos(\frac{3}{50}x^{2})}{25} - \frac{6x({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln^{2}(3)sin(x)cos(\frac{3}{50}x^{2})}{25} - \frac{6x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*2ln(3)*0sin(x)cos(\frac{3}{50}x^{2})}{25(3)} - \frac{6x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)cos(x)cos(\frac{3}{50}x^{2})}{25} - \frac{6x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(x)*-sin(\frac{3}{50}x^{2})*\frac{3}{50}*2x}{25} - \frac{9*2x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)sin(\frac{3}{50}x^{2})}{625} - \frac{9x^{2}({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln(3)sin(\frac{3}{50}x^{2})}{625} - \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*0sin(\frac{3}{50}x^{2})}{625(3)} - \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x}{625} + ({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln^{2}(3)sin^{2}(x) + \frac{{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*2ln(3)*0sin^{2}(x)}{(3)} + {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)*2sin(x)cos(x) - ({3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}((cos(\frac{3}{50}x^{2})*\frac{3}{50}*2x + -sin(x))ln(3) + \frac{(sin(\frac{3}{50}x^{2}) + cos(x))(0)}{(3)}))ln(3)cos(x) - \frac{{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}*0cos(x)}{(3)} - {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)*-sin(x)\\=& - \frac{6x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)cos(x)cos(\frac{3}{50}x^{2})}{25} - \frac{9 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(x)cos(\frac{3}{50}x^{2})}{25} - \frac{3x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)cos(\frac{3}{50}x^{2})cos(x)}{25} + \frac{27x^{3}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{3}(3)cos^{3}(\frac{3}{50}x^{2})}{15625} - \frac{27x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{3}(3)sin(x)cos^{2}(\frac{3}{50}x^{2})}{625} - \frac{81x^{3}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(\frac{3}{50}x^{2})cos(\frac{3}{50}x^{2})}{15625} + \frac{9x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{3}(3)sin^{2}(x)cos(\frac{3}{50}x^{2})}{25} + \frac{18x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(\frac{3}{50}x^{2})sin(x)}{625} + \frac{9x^{2}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(x)sin(\frac{3}{50}x^{2})}{625} - \frac{27x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)sin(\frac{3}{50}x^{2})}{625} - \frac{27x^{3}{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)cos(\frac{3}{50}x^{2})}{15625} + 3 * {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)sin(x)cos(x) - {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{3}(3)sin^{3}(x) + \frac{27x{3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln^{2}(3)cos^{2}(\frac{3}{50}x^{2})}{625} + {3}^{(sin(\frac{3}{50}x^{2}) + cos(x))}ln(3)sin(x)\\ \end{split}\end{equation} \]
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