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。\[ \begin{equation}\begin{split}【1/1】求函数cosh(1 - sqrt(arcsin(x)))sqrt(πx) 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(πx)cosh(-sqrt(arcsin(x)) + 1)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( sqrt(πx)cosh(-sqrt(arcsin(x)) + 1)\right)}{dx}\\=&\frac{π*\frac{1}{2}cosh(-sqrt(arcsin(x)) + 1)}{(πx)^{\frac{1}{2}}} + sqrt(πx)sinh(-sqrt(arcsin(x)) + 1)(\frac{-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})*\frac{1}{2}}{(arcsin(x))^{\frac{1}{2}}} + 0)\\=&\frac{π^{\frac{1}{2}}cosh(-sqrt(arcsin(x)) + 1)}{2x^{\frac{1}{2}}} - \frac{sqrt(πx)sinh(-sqrt(arcsin(x)) + 1)}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{π^{\frac{1}{2}}cosh(-sqrt(arcsin(x)) + 1)}{2x^{\frac{1}{2}}} - \frac{sqrt(πx)sinh(-sqrt(arcsin(x)) + 1)}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)}\right)}{dx}\\=&\frac{π^{\frac{1}{2}}*\frac{-1}{2}cosh(-sqrt(arcsin(x)) + 1)}{2x^{\frac{3}{2}}} + \frac{π^{\frac{1}{2}}sinh(-sqrt(arcsin(x)) + 1)(\frac{-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})*\frac{1}{2}}{(arcsin(x))^{\frac{1}{2}}} + 0)}{2x^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})sqrt(πx)sinh(-sqrt(arcsin(x)) + 1)}{2arcsin^{\frac{1}{2}}(x)} - \frac{(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})sqrt(πx)sinh(-sqrt(arcsin(x)) + 1)}{2(-x^{2} + 1)^{\frac{1}{2}}} - \frac{π*\frac{1}{2}sinh(-sqrt(arcsin(x)) + 1)}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)(πx)^{\frac{1}{2}}} - \frac{sqrt(πx)cosh(-sqrt(arcsin(x)) + 1)(\frac{-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})*\frac{1}{2}}{(arcsin(x))^{\frac{1}{2}}} + 0)}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)}\\=&\frac{-π^{\frac{1}{2}}cosh(-sqrt(arcsin(x)) + 1)}{4x^{\frac{3}{2}}} - \frac{π^{\frac{1}{2}}sinh(-sqrt(arcsin(x)) + 1)}{4(-x^{2} + 1)^{\frac{1}{2}}x^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{xsqrt(πx)sinh(-sqrt(arcsin(x)) + 1)}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{sqrt(πx)sinh(-sqrt(arcsin(x)) + 1)}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{π^{\frac{1}{2}}sinh(-sqrt(arcsin(x)) + 1)}{4(-x^{2} + 1)^{\frac{1}{2}}x^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{sqrt(πx)cosh(-sqrt(arcsin(x)) + 1)}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin(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!