There are 1 questions in this calculation: for each question, the 4 derivative of h is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ arcsin(h)h\ with\ respect\ to\ h：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = harcsin(h)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( harcsin(h)\right)}{dh}\\=&arcsin(h) + h(\frac{(1)}{((1 - (h)^{2})^{\frac{1}{2}})})\\=&arcsin(h) + \frac{h}{(-h^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( arcsin(h) + \frac{h}{(-h^{2} + 1)^{\frac{1}{2}}}\right)}{dh}\\=&(\frac{(1)}{((1 - (h)^{2})^{\frac{1}{2}})}) + (\frac{\frac{-1}{2}(-2h + 0)}{(-h^{2} + 1)^{\frac{3}{2}}})h + \frac{1}{(-h^{2} + 1)^{\frac{1}{2}}}\\=&\frac{h^{2}}{(-h^{2} + 1)^{\frac{3}{2}}} + \frac{1}{(-h^{2} + 1)^{\frac{1}{2}}} + \frac{1}{(-h^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{h^{2}}{(-h^{2} + 1)^{\frac{3}{2}}} + \frac{1}{(-h^{2} + 1)^{\frac{1}{2}}} + \frac{1}{(-h^{2} + 1)^{\frac{1}{2}}}\right)}{dh}\\=&(\frac{\frac{-3}{2}(-2h + 0)}{(-h^{2} + 1)^{\frac{5}{2}}})h^{2} + \frac{2h}{(-h^{2} + 1)^{\frac{3}{2}}} + (\frac{\frac{-1}{2}(-2h + 0)}{(-h^{2} + 1)^{\frac{3}{2}}}) + (\frac{\frac{-1}{2}(-2h + 0)}{(-h^{2} + 1)^{\frac{3}{2}}})\\=&\frac{3h^{3}}{(-h^{2} + 1)^{\frac{5}{2}}} + \frac{4h}{(-h^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3h^{3}}{(-h^{2} + 1)^{\frac{5}{2}}} + \frac{4h}{(-h^{2} + 1)^{\frac{3}{2}}}\right)}{dh}\\=&3(\frac{\frac{-5}{2}(-2h + 0)}{(-h^{2} + 1)^{\frac{7}{2}}})h^{3} + \frac{3*3h^{2}}{(-h^{2} + 1)^{\frac{5}{2}}} + 4(\frac{\frac{-3}{2}(-2h + 0)}{(-h^{2} + 1)^{\frac{5}{2}}})h + \frac{4}{(-h^{2} + 1)^{\frac{3}{2}}}\\=&\frac{15h^{4}}{(-h^{2} + 1)^{\frac{7}{2}}} + \frac{21h^{2}}{(-h^{2} + 1)^{\frac{5}{2}}} + \frac{4}{(-h^{2} + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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