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

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