There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (x + 15){(x + 1)}^{2}{\frac{1}{(x - 6)}}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x - 6)^{4}} + \frac{17x^{2}}{(x - 6)^{4}} + \frac{31x}{(x - 6)^{4}} + \frac{15}{(x - 6)^{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x - 6)^{4}} + \frac{17x^{2}}{(x - 6)^{4}} + \frac{31x}{(x - 6)^{4}} + \frac{15}{(x - 6)^{4}}\right)}{dx}\\=&(\frac{-4(1 + 0)}{(x - 6)^{5}})x^{3} + \frac{3x^{2}}{(x - 6)^{4}} + 17(\frac{-4(1 + 0)}{(x - 6)^{5}})x^{2} + \frac{17*2x}{(x - 6)^{4}} + 31(\frac{-4(1 + 0)}{(x - 6)^{5}})x + \frac{31}{(x - 6)^{4}} + 15(\frac{-4(1 + 0)}{(x - 6)^{5}})\\=&\frac{-4x^{3}}{(x - 6)^{5}} + \frac{3x^{2}}{(x - 6)^{4}} - \frac{68x^{2}}{(x - 6)^{5}} + \frac{34x}{(x - 6)^{4}} - \frac{124x}{(x - 6)^{5}} - \frac{60}{(x - 6)^{5}} + \frac{31}{(x - 6)^{4}}\\ \end{split}\end{equation} \]

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