There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({(6x)}^{\frac{1}{2}} + 13x)}^{-6}{(5{x}^{6} - 5x)}^{6}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(5x^{6} - 5x)^{6}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(5x^{6} - 5x)^{6}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}}\right)}{dx}\\=&(\frac{-6(\frac{6^{\frac{1}{2}}*\frac{1}{2}}{x^{\frac{1}{2}}} + 13)}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{7}})(5x^{6} - 5x)^{6} + \frac{(6(5x^{6} - 5x)^{5}(5*6x^{5} - 5))}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}}\\=&\frac{-3*6^{\frac{1}{2}}(5x^{6} - 5x)^{6}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{7}x^{\frac{1}{2}}} - \frac{78(5x^{6} - 5x)^{6}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{7}} + \frac{562500x^{35}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}} - \frac{2906250x^{30}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}} + \frac{6093750x^{25}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}} - \frac{6562500x^{20}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}} + \frac{3750000x^{15}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}} - \frac{1031250x^{10}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}} + \frac{93750x^{5}}{(6^{\frac{1}{2}}x^{\frac{1}{2}} + 13x)^{6}}\\ \end{split}\end{equation} \]

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