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。\[ \begin{equation}\begin{split}【1/1】求函数-sqrt(1 - {x}^{2})(tan(x) + x{\frac{1}{(cos(x))}}^{2}) 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = -tan(x)sqrt(-x^{2} + 1) - \frac{xsqrt(-x^{2} + 1)}{cos^{2}(x)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( -tan(x)sqrt(-x^{2} + 1) - \frac{xsqrt(-x^{2} + 1)}{cos^{2}(x)}\right)}{dx}\\=&-sec^{2}(x)(1)sqrt(-x^{2} + 1) - \frac{tan(x)(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{sqrt(-x^{2} + 1)}{cos^{2}(x)} - \frac{x*2sin(x)sqrt(-x^{2} + 1)}{cos^{3}(x)} - \frac{x(-2x + 0)*\frac{1}{2}}{cos^{2}(x)(-x^{2} + 1)^{\frac{1}{2}}}\\=&-sqrt(-x^{2} + 1)sec^{2}(x) + \frac{xtan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{sqrt(-x^{2} + 1)}{cos^{2}(x)} - \frac{2xsin(x)sqrt(-x^{2} + 1)}{cos^{3}(x)} + \frac{x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}cos^{2}(x)}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!