There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(x - 1)}^{5})}{({(10x - 6)}^{9})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{5}}{(10x - 6)^{9}} - \frac{5x^{4}}{(10x - 6)^{9}} + \frac{10x^{3}}{(10x - 6)^{9}} - \frac{10x^{2}}{(10x - 6)^{9}} + \frac{5x}{(10x - 6)^{9}} - \frac{1}{(10x - 6)^{9}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{5}}{(10x - 6)^{9}} - \frac{5x^{4}}{(10x - 6)^{9}} + \frac{10x^{3}}{(10x - 6)^{9}} - \frac{10x^{2}}{(10x - 6)^{9}} + \frac{5x}{(10x - 6)^{9}} - \frac{1}{(10x - 6)^{9}}\right)}{dx}\\=&(\frac{-9(10 + 0)}{(10x - 6)^{10}})x^{5} + \frac{5x^{4}}{(10x - 6)^{9}} - 5(\frac{-9(10 + 0)}{(10x - 6)^{10}})x^{4} - \frac{5*4x^{3}}{(10x - 6)^{9}} + 10(\frac{-9(10 + 0)}{(10x - 6)^{10}})x^{3} + \frac{10*3x^{2}}{(10x - 6)^{9}} - 10(\frac{-9(10 + 0)}{(10x - 6)^{10}})x^{2} - \frac{10*2x}{(10x - 6)^{9}} + 5(\frac{-9(10 + 0)}{(10x - 6)^{10}})x + \frac{5}{(10x - 6)^{9}} - (\frac{-9(10 + 0)}{(10x - 6)^{10}})\\=&\frac{-90x^{5}}{(10x - 6)^{10}} + \frac{5x^{4}}{(10x - 6)^{9}} + \frac{450x^{4}}{(10x - 6)^{10}} - \frac{20x^{3}}{(10x - 6)^{9}} - \frac{900x^{3}}{(10x - 6)^{10}} + \frac{30x^{2}}{(10x - 6)^{9}} + \frac{900x^{2}}{(10x - 6)^{10}} - \frac{20x}{(10x - 6)^{9}} - \frac{450x}{(10x - 6)^{10}} + \frac{5}{(10x - 6)^{9}} + \frac{90}{(10x - 6)^{10}}\\ \end{split}\end{equation} \]

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