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。\[ \begin{equation}\begin{split}【1/1】求函数arctan(666x) 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( arctan(666x)\right)}{dx}\\=&(\frac{(666)}{(1 + (666x)^{2})})\\=&\frac{666}{(443556x^{2} + 1)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{666}{(443556x^{2} + 1)}\right)}{dx}\\=&666(\frac{-(443556*2x + 0)}{(443556x^{2} + 1)^{2}})\\=&\frac{-590816592x}{(443556x^{2} + 1)^{2}}\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( \frac{-590816592x}{(443556x^{2} + 1)^{2}}\right)}{dx}\\=&-590816592(\frac{-2(443556*2x + 0)}{(443556x^{2} + 1)^{3}})x - \frac{590816592}{(443556x^{2} + 1)^{2}}\\=&\frac{1048240977124608x^{2}}{(443556x^{2} + 1)^{3}} - \frac{590816592}{(443556x^{2} + 1)^{2}}\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( \frac{1048240977124608x^{2}}{(443556x^{2} + 1)^{3}} - \frac{590816592}{(443556x^{2} + 1)^{2}}\right)}{dx}\\=&1048240977124608(\frac{-3(443556*2x + 0)}{(443556x^{2} + 1)^{4}})x^{2} + \frac{1048240977124608*2x}{(443556x^{2} + 1)^{3}} - 590816592(\frac{-2(443556*2x + 0)}{(443556x^{2} + 1)^{3}})\\=&\frac{-4263093966753462272x^{3}}{(443556x^{2} + 1)^{4}} + \frac{3144722931373824x}{(443556x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!