本次共计算 1 个题目:每一题对 x 求 1 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数{x}^{2}sqrt(ln({x}^{7} - tan(\frac{1}{(1 - {x}^{(x - {\frac{1}{x}}^{5})})})) + 1) 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{2}sqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( x^{2}sqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)\right)}{dx}\\=&2xsqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1) + \frac{x^{2}(\frac{(7x^{6} - sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})((\frac{-(-({x}^{(x - \frac{1}{x^{5}})}((1 - \frac{-5}{x^{6}})ln(x) + \frac{(x - \frac{1}{x^{5}})(1)}{(x)})) + 0)}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}})))}{(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))} + 0)*\frac{1}{2}}{(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}}\\=&2xsqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1) + \frac{7x^{8}}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}} - \frac{5{x}^{(x - \frac{1}{x^{5}})}ln(x)sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}x^{4}} - \frac{x^{2}{x}^{(x - \frac{1}{x^{5}})}ln(x)sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}} - \frac{x^{2}{x}^{(x - \frac{1}{x^{5}})}sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}} + \frac{{x}^{(x - \frac{1}{x^{5}})}sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}x^{4}}\\ \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!