本次共计算 1 个题目:每一题对 x 求 2 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数{x}^{x} - {(arcsin(x))}^{x} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {x}^{x} - {arcsin(x)}^{x}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( {x}^{x} - {arcsin(x)}^{x}\right)}{dx}\\=&({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})) - ({arcsin(x)}^{x}((1)ln(arcsin(x)) + \frac{(x)((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))}{(arcsin(x))}))\\=&{x}^{x}ln(x) - {arcsin(x)}^{x}ln(arcsin(x)) + {x}^{x} - \frac{x{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( {x}^{x}ln(x) - {arcsin(x)}^{x}ln(arcsin(x)) + {x}^{x} - \frac{x{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)}\right)}{dx}\\=&({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x) + \frac{{x}^{x}}{(x)} - ({arcsin(x)}^{x}((1)ln(arcsin(x)) + \frac{(x)((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))}{(arcsin(x))}))ln(arcsin(x)) - \frac{{arcsin(x)}^{x}(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(arcsin(x))} + ({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})) - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x{arcsin(x)}^{x}}{arcsin(x)} - \frac{{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)} - \frac{x({arcsin(x)}^{x}((1)ln(arcsin(x)) + \frac{(x)((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))}{(arcsin(x))}))}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)} - \frac{x{arcsin(x)}^{x}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}}\\=&{x}^{x}ln^{2}(x) - {arcsin(x)}^{x}ln^{2}(arcsin(x)) + \frac{{x}^{x}}{x} + 2{x}^{x}ln(x) - \frac{x{arcsin(x)}^{x}ln(arcsin(x))}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)} - \frac{{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)} - \frac{{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)} - \frac{x^{2}{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin(x)} + {x}^{x} - \frac{x{arcsin(x)}^{x}ln(arcsin(x))}{(-x^{2} + 1)^{\frac{1}{2}}arcsin(x)} - \frac{x^{2}{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)} + \frac{x{arcsin(x)}^{x}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{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!