本次共计算 1 个题目:每一题对 x 求 5 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数cos(sin(arctan(x))) 关于 x 的 5 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 5 阶导数:} \\=&\frac{420x^{2}sin(arctan(x))cos(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{60sin(arctan(x))cos(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{4}} - \frac{80xcos^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{60xsin^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{120xsin(arctan(x))sin(sin(arctan(x)))cos^{2}(arctan(x))}{(x^{2} + 1)^{5}} + \frac{288x^{2}sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{4}} - \frac{10sin(arctan(x))cos^{3}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{160xcos^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{4}} + \frac{400x^{3}cos^{2}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{140x^{2}sin(sin(arctan(x)))cos^{3}(arctan(x))}{(x^{2} + 1)^{5}} - \frac{400x^{3}sin(arctan(x))sin(sin(arctan(x)))}{(x^{2} + 1)^{5}} + \frac{160xsin(arctan(x))sin(sin(arctan(x)))}{(x^{2} + 1)^{4}} + \frac{140x^{2}sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}} - \frac{384x^{4}sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}} - \frac{15sin(arctan(x))cos(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{24sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{3}} - \frac{10sin(sin(arctan(x)))cos^{3}(arctan(x))}{(x^{2} + 1)^{5}} + \frac{3sin^{2}(arctan(x))sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}} + \frac{12sin(sin(arctan(x)))sin^{2}(arctan(x))cos(arctan(x))}{(x^{2} + 1)^{5}} - \frac{20sin(sin(arctan(x)))cos^{3}(arctan(x))}{(x^{2} + 1)^{4}} - \frac{20xcos^{4}(arctan(x))cos(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{20sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{4}} + \frac{20xsin(arctan(x))sin(sin(arctan(x)))}{(x^{2} + 1)^{5}} - \frac{sin(sin(arctan(x)))cos^{5}(arctan(x))}{(x^{2} + 1)^{5}} - \frac{sin(sin(arctan(x)))cos(arctan(x))}{(x^{2} + 1)^{5}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!