There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ Aarcsin(wx + r) + B\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( Aarcsin(wx + r) + B\right)}{dx}\\=&A(\frac{(w + 0)}{((1 - (wx + r)^{2})^{\frac{1}{2}})}) + 0\\=&\frac{Aw}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{Aw}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}})Aw + 0\\=&\frac{Aw^{3}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + \frac{Aw^{2}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{Aw^{3}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + \frac{Aw^{2}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{3}x + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}} + (\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{2}r + 0\\=&\frac{3Aw^{5}x^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{6Aw^{4}rx}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{3Aw^{3}r^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3Aw^{5}x^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{6Aw^{4}rx}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{3Aw^{3}r^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{Aw^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{5}x^{2} + \frac{3Aw^{5}*2x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + 6(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{4}rx + \frac{6Aw^{4}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + 3(\frac{\frac{-5}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}})Aw^{3}r^{2} + 0 + (\frac{\frac{-3}{2}(-w^{2}*2x - 2wr + 0 + 0)}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}})Aw^{3} + 0\\=&\frac{15Aw^{7}x^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{45Aw^{6}rx^{2}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{9Aw^{5}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{45Aw^{5}r^{2}x}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}} + \frac{9Aw^{4}r}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{5}{2}}} + \frac{15Aw^{4}r^{3}}{(-w^{2}x^{2} - 2wrx - r^{2} + 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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