There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ arcsin(5{x}^{2} + 3{y}^{4})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(5x^{2} + 3y^{4})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(5x^{2} + 3y^{4})\right)}{dx}\\=&(\frac{(5*2x + 0)}{((1 - (5x^{2} + 3y^{4})^{2})^{\frac{1}{2}})})\\=&\frac{10x}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{10x}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&10(\frac{\frac{-1}{2}(-25*4x^{3} - 30y^{4}*2x + 0 + 0)}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}})x + \frac{10}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{1}{2}}}\\=&\frac{500x^{4}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}} + \frac{300y^{4}x^{2}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}} + \frac{10}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{500x^{4}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}} + \frac{300y^{4}x^{2}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}} + \frac{10}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&500(\frac{\frac{-3}{2}(-25*4x^{3} - 30y^{4}*2x + 0 + 0)}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{5}{2}}})x^{4} + \frac{500*4x^{3}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}} + 300(\frac{\frac{-3}{2}(-25*4x^{3} - 30y^{4}*2x + 0 + 0)}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{5}{2}}})y^{4}x^{2} + \frac{300y^{4}*2x}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}} + 10(\frac{\frac{-1}{2}(-25*4x^{3} - 30y^{4}*2x + 0 + 0)}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}})\\=&\frac{75000x^{7}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{5}{2}}} + \frac{90000y^{4}x^{5}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{5}{2}}} + \frac{2500x^{3}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}} + \frac{27000y^{8}x^{3}}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{5}{2}}} + \frac{900y^{4}x}{(-25x^{4} - 30y^{4}x^{2} - 9y^{8} + 1)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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