There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sqrt((p - a)(p - b)(p - c)(p - d) - abcdcos(\frac{(a + c)}{2}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(-p^{3}d + p^{2}cd - p^{3}c + p^{2}bd - pbcd + p^{2}bc - p^{3}b + p^{2}ad - pacd + p^{2}ac - pabd - pabc + p^{2}ab - p^{3}a + p^{4} - abcdcos(\frac{1}{2}a + \frac{1}{2}c) + abcd)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(-p^{3}d + p^{2}cd - p^{3}c + p^{2}bd - pbcd + p^{2}bc - p^{3}b + p^{2}ad - pacd + p^{2}ac - pabd - pabc + p^{2}ab - p^{3}a + p^{4} - abcdcos(\frac{1}{2}a + \frac{1}{2}c) + abcd)\right)}{dx}\\=&\frac{(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 - abcd*-sin(\frac{1}{2}a + \frac{1}{2}c)(0 + 0) + 0)*\frac{1}{2}}{(-p^{3}d + p^{2}cd - p^{3}c + p^{2}bd - pbcd + p^{2}bc - p^{3}b + p^{2}ad - pacd + p^{2}ac - pabd - pabc + p^{2}ab - p^{3}a + p^{4} - abcdcos(\frac{1}{2}a + \frac{1}{2}c) + abcd)^{\frac{1}{2}}}\\=&\frac{0}{2}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{0}{2}\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]

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