There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sqrt({\frac{1}{(ax + ab + bc + abcx)}}^{5})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{1}{(ax + abcx + bc + ab)^{5}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{1}{(ax + abcx + bc + ab)^{5}})\right)}{dx}\\=&\frac{(\frac{-5(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{6}})*\frac{1}{2}}{(\frac{1}{(ax + abcx + bc + ab)^{5}})^{\frac{1}{2}}}\\=& - \frac{5abc}{2(ax + abcx + bc + ab)^{\frac{7}{2}}} - \frac{5a}{2(ax + abcx + bc + ab)^{\frac{7}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{5abc}{2(ax + abcx + bc + ab)^{\frac{7}{2}}} - \frac{5a}{2(ax + abcx + bc + ab)^{\frac{7}{2}}}\right)}{dx}\\=& - \frac{5(\frac{\frac{-7}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{9}{2}}})abc}{2} + 0 - \frac{5(\frac{\frac{-7}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{9}{2}}})a}{2} + 0\\=&\frac{35a^{2}b^{2}c^{2}}{4(ax + abcx + bc + ab)^{\frac{9}{2}}} + \frac{35a^{2}bc}{2(ax + abcx + bc + ab)^{\frac{9}{2}}} + \frac{35a^{2}}{4(ax + abcx + bc + ab)^{\frac{9}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{35a^{2}b^{2}c^{2}}{4(ax + abcx + bc + ab)^{\frac{9}{2}}} + \frac{35a^{2}bc}{2(ax + abcx + bc + ab)^{\frac{9}{2}}} + \frac{35a^{2}}{4(ax + abcx + bc + ab)^{\frac{9}{2}}}\right)}{dx}\\=&\frac{35(\frac{\frac{-9}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{11}{2}}})a^{2}b^{2}c^{2}}{4} + 0 + \frac{35(\frac{\frac{-9}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{11}{2}}})a^{2}bc}{2} + 0 + \frac{35(\frac{\frac{-9}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{11}{2}}})a^{2}}{4} + 0\\=& - \frac{315a^{3}b^{3}c^{3}}{8(ax + abcx + bc + ab)^{\frac{11}{2}}} - \frac{945a^{3}b^{2}c^{2}}{8(ax + abcx + bc + ab)^{\frac{11}{2}}} - \frac{945a^{3}bc}{8(ax + abcx + bc + ab)^{\frac{11}{2}}} - \frac{315a^{3}}{8(ax + abcx + bc + ab)^{\frac{11}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{315a^{3}b^{3}c^{3}}{8(ax + abcx + bc + ab)^{\frac{11}{2}}} - \frac{945a^{3}b^{2}c^{2}}{8(ax + abcx + bc + ab)^{\frac{11}{2}}} - \frac{945a^{3}bc}{8(ax + abcx + bc + ab)^{\frac{11}{2}}} - \frac{315a^{3}}{8(ax + abcx + bc + ab)^{\frac{11}{2}}}\right)}{dx}\\=& - \frac{315(\frac{\frac{-11}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{13}{2}}})a^{3}b^{3}c^{3}}{8} + 0 - \frac{945(\frac{\frac{-11}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{13}{2}}})a^{3}b^{2}c^{2}}{8} + 0 - \frac{945(\frac{\frac{-11}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{13}{2}}})a^{3}bc}{8} + 0 - \frac{315(\frac{\frac{-11}{2}(a + abc + 0 + 0)}{(ax + abcx + bc + ab)^{\frac{13}{2}}})a^{3}}{8} + 0\\=&\frac{3465a^{4}b^{4}c^{4}}{16(ax + abcx + bc + ab)^{\frac{13}{2}}} + \frac{3465a^{4}b^{3}c^{3}}{4(ax + abcx + bc + ab)^{\frac{13}{2}}} + \frac{10395a^{4}b^{2}c^{2}}{8(ax + abcx + bc + ab)^{\frac{13}{2}}} + \frac{3465a^{4}bc}{4(ax + abcx + bc + ab)^{\frac{13}{2}}} + \frac{3465a^{4}}{16(ax + abcx + bc + ab)^{\frac{13}{2}}}\\ \end{split}\end{equation} \]

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