There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {2}^{arcsin(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {2}^{arcsin(x)}\right)}{dx}\\=&({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))\\=&\frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln(2) + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x{2}^{arcsin(x)}ln(2) + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{3}{2}}(2)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{3x^{2}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{2}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}{2}^{arcsin(x)}ln(2) + \frac{3*2x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{5}{2}}(2)} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}}){2}^{arcsin(x)}ln(2) + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{3}{2}}(2)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{x{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}(2)} + 2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x{2}^{arcsin(x)}ln^{2}(2) + \frac{2 * {2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{2x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{2x{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{2}(2)} + \frac{(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}}){2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)} + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*3ln^{2}(2)*0}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{15x^{3}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12x^{2}{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{3}} + \frac{3 * {2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{3x{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3x{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln^{4}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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