There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{x}^{6}}{(x + {x}^{2} + {x}^{3} + {x}^{4} + {x}^{5})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})}\right)}{dx}\\=&(\frac{-(1 + 2x + 3x^{2} + 4x^{3} + 5x^{4})}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}})x^{6} + \frac{6x^{5}}{(x + x^{2} + x^{3} + x^{4} + x^{5})}\\=&\frac{-2x^{7}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} - \frac{3x^{8}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} - \frac{4x^{9}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} - \frac{5x^{10}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} - \frac{x^{6}}{(x + x^{2} + x^{3} + x^{4} + x^{5})^{2}} + \frac{6x^{5}}{(x + x^{2} + x^{3} + x^{4} + x^{5})}\\ \end{split}\end{equation} \]

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