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。
\[ \begin{equation}\begin{split}【1/1】求函数th(x*333x*4) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = th(1332x^{2})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( th(1332x^{2})\right)}{dx}\\=&(1 - th^{2}(1332x^{2}))*1332*2x\\=& - 2664xth^{2}(1332x^{2}) + 2664x\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( - 2664xth^{2}(1332x^{2}) + 2664x\right)}{dx}\\=& - 2664th^{2}(1332x^{2}) - 2664x*2th(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x + 2664\\=& - 2664th^{2}(1332x^{2}) - 14193792x^{2}th(1332x^{2}) + 14193792x^{2}th^{3}(1332x^{2}) + 2664\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - 2664th^{2}(1332x^{2}) - 14193792x^{2}th(1332x^{2}) + 14193792x^{2}th^{3}(1332x^{2}) + 2664\right)}{dx}\\=& - 2664*2th(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x - 14193792*2xth(1332x^{2}) - 14193792x^{2}(1 - th^{2}(1332x^{2}))*1332*2x + 14193792*2xth^{3}(1332x^{2}) + 14193792x^{2}*3th^{2}(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x + 0\\=& - 42581376xth(1332x^{2}) + 42581376xth^{3}(1332x^{2}) + 151249047552x^{3}th^{2}(1332x^{2}) - 113436785664x^{3}th^{4}(1332x^{2}) - 37812261888x^{3}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 42581376xth(1332x^{2}) + 42581376xth^{3}(1332x^{2}) + 151249047552x^{3}th^{2}(1332x^{2}) - 113436785664x^{3}th^{4}(1332x^{2}) - 37812261888x^{3}\right)}{dx}\\=& - 42581376th(1332x^{2}) - 42581376x(1 - th^{2}(1332x^{2}))*1332*2x + 42581376th^{3}(1332x^{2}) + 42581376x*3th^{2}(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x + 151249047552*3x^{2}th^{2}(1332x^{2}) + 151249047552x^{3}*2th(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x - 113436785664*3x^{2}th^{4}(1332x^{2}) - 113436785664x^{3}*4th^{3}(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x - 37812261888*3x^{2}\\=& - 42581376th(1332x^{2}) + 907494285312x^{2}th^{2}(1332x^{2}) - 680620713984x^{2}th^{4}(1332x^{2}) + 42581376th^{3}(1332x^{2}) + 805854925357056x^{4}th(1332x^{2}) - 2014637313392640x^{4}th^{3}(1332x^{2}) + 1208782388035584x^{4}th^{5}(1332x^{2}) - 226873571328x^{2}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数th(x*333x*4) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = th(1332x^{2})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( th(1332x^{2})\right)}{dx}\\=&(1 - th^{2}(1332x^{2}))*1332*2x\\=& - 2664xth^{2}(1332x^{2}) + 2664x\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( - 2664xth^{2}(1332x^{2}) + 2664x\right)}{dx}\\=& - 2664th^{2}(1332x^{2}) - 2664x*2th(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x + 2664\\=& - 2664th^{2}(1332x^{2}) - 14193792x^{2}th(1332x^{2}) + 14193792x^{2}th^{3}(1332x^{2}) + 2664\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - 2664th^{2}(1332x^{2}) - 14193792x^{2}th(1332x^{2}) + 14193792x^{2}th^{3}(1332x^{2}) + 2664\right)}{dx}\\=& - 2664*2th(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x - 14193792*2xth(1332x^{2}) - 14193792x^{2}(1 - th^{2}(1332x^{2}))*1332*2x + 14193792*2xth^{3}(1332x^{2}) + 14193792x^{2}*3th^{2}(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x + 0\\=& - 42581376xth(1332x^{2}) + 42581376xth^{3}(1332x^{2}) + 151249047552x^{3}th^{2}(1332x^{2}) - 113436785664x^{3}th^{4}(1332x^{2}) - 37812261888x^{3}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 42581376xth(1332x^{2}) + 42581376xth^{3}(1332x^{2}) + 151249047552x^{3}th^{2}(1332x^{2}) - 113436785664x^{3}th^{4}(1332x^{2}) - 37812261888x^{3}\right)}{dx}\\=& - 42581376th(1332x^{2}) - 42581376x(1 - th^{2}(1332x^{2}))*1332*2x + 42581376th^{3}(1332x^{2}) + 42581376x*3th^{2}(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x + 151249047552*3x^{2}th^{2}(1332x^{2}) + 151249047552x^{3}*2th(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x - 113436785664*3x^{2}th^{4}(1332x^{2}) - 113436785664x^{3}*4th^{3}(1332x^{2})(1 - th^{2}(1332x^{2}))*1332*2x - 37812261888*3x^{2}\\=& - 42581376th(1332x^{2}) + 907494285312x^{2}th^{2}(1332x^{2}) - 680620713984x^{2}th^{4}(1332x^{2}) + 42581376th^{3}(1332x^{2}) + 805854925357056x^{4}th(1332x^{2}) - 2014637313392640x^{4}th^{3}(1332x^{2}) + 1208782388035584x^{4}th^{5}(1332x^{2}) - 226873571328x^{2}\\ \end{split}\end{equation} \]
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