There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ abs + (arcsin(x)) - {(7cos(x))}^{\frac{3}{10}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = abs + arcsin(x) - 7^{\frac{3}{10}}cos^{\frac{3}{10}}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( abs + arcsin(x) - 7^{\frac{3}{10}}cos^{\frac{3}{10}}(x)\right)}{dx}\\=&0 + (\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}) - \frac{7^{\frac{3}{10}}*\frac{-3}{10}sin(x)}{cos^{\frac{7}{10}}(x)}\\=&\frac{1}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{7^{\frac{3}{10}}*3sin(x)}{10cos^{\frac{7}{10}}(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{7^{\frac{3}{10}}*3sin(x)}{10cos^{\frac{7}{10}}(x)}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}) + \frac{7^{\frac{3}{10}}*3cos(x)}{10cos^{\frac{7}{10}}(x)} + \frac{7^{\frac{3}{10}}*3sin(x)*\frac{7}{10}sin(x)}{10cos^{\frac{17}{10}}(x)}\\=&\frac{x}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{7^{\frac{3}{10}}*3cos^{\frac{3}{10}}(x)}{10} + \frac{7^{\frac{3}{10}}*21sin^{2}(x)}{100cos^{\frac{17}{10}}(x)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{7^{\frac{3}{10}}*3cos^{\frac{3}{10}}(x)}{10} + \frac{7^{\frac{3}{10}}*21sin^{2}(x)}{100cos^{\frac{17}{10}}(x)}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{7^{\frac{3}{10}}*3*\frac{-3}{10}sin(x)}{10cos^{\frac{7}{10}}(x)} + \frac{7^{\frac{3}{10}}*21*2sin(x)cos(x)}{100cos^{\frac{17}{10}}(x)} + \frac{7^{\frac{3}{10}}*21sin^{2}(x)*\frac{17}{10}sin(x)}{100cos^{\frac{27}{10}}(x)}\\=&\frac{3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{7^{\frac{3}{10}}*21sin(x)}{50cos^{\frac{7}{10}}(x)} - \frac{7^{\frac{3}{10}}*9sin(x)}{100cos^{\frac{7}{10}}(x)} + \frac{7^{\frac{3}{10}}*357sin^{3}(x)}{1000cos^{\frac{27}{10}}(x)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{7^{\frac{3}{10}}*21sin(x)}{50cos^{\frac{7}{10}}(x)} - \frac{7^{\frac{3}{10}}*9sin(x)}{100cos^{\frac{7}{10}}(x)} + \frac{7^{\frac{3}{10}}*357sin^{3}(x)}{1000cos^{\frac{27}{10}}(x)}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2} + \frac{3*2x}{(-x^{2} + 1)^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}}) + \frac{7^{\frac{3}{10}}*21cos(x)}{50cos^{\frac{7}{10}}(x)} + \frac{7^{\frac{3}{10}}*21sin(x)*\frac{7}{10}sin(x)}{50cos^{\frac{17}{10}}(x)} - \frac{7^{\frac{3}{10}}*9cos(x)}{100cos^{\frac{7}{10}}(x)} - \frac{7^{\frac{3}{10}}*9sin(x)*\frac{7}{10}sin(x)}{100cos^{\frac{17}{10}}(x)} + \frac{7^{\frac{3}{10}}*357*3sin^{2}(x)cos(x)}{1000cos^{\frac{27}{10}}(x)} + \frac{7^{\frac{3}{10}}*357sin^{3}(x)*\frac{27}{10}sin(x)}{1000cos^{\frac{37}{10}}(x)}\\=&\frac{15x^{3}}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{7^{\frac{3}{10}}*21cos^{\frac{3}{10}}(x)}{50} + \frac{7^{\frac{3}{10}}*147sin^{2}(x)}{500cos^{\frac{17}{10}}(x)} - \frac{7^{\frac{3}{10}}*9cos^{\frac{3}{10}}(x)}{100} - \frac{7^{\frac{3}{10}}*63sin^{2}(x)}{1000cos^{\frac{17}{10}}(x)} + \frac{7^{\frac{3}{10}}*1071sin^{2}(x)}{1000cos^{\frac{17}{10}}(x)} + \frac{7^{\frac{3}{10}}*9639sin^{4}(x)}{10000cos^{\frac{37}{10}}(x)}\\ \end{split}\end{equation} \]

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