There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ cosh(1 - sqrt(arcsin(x)))sqrt(πx)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(πx)cosh(-sqrt(arcsin(x)) + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\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}{The\ second\ derivative\ of\ function:} \\&\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} \]

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