There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{ln(x)}{({x}^{7} + 7)} - ln(x){x}^{7} + \frac{{x}^{7}}{7}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{ln(x)}{(x^{7} + 7)} - x^{7}ln(x) + \frac{1}{7}x^{7}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{ln(x)}{(x^{7} + 7)} - x^{7}ln(x) + \frac{1}{7}x^{7}\right)}{dx}\\=&(\frac{-(7x^{6} + 0)}{(x^{7} + 7)^{2}})ln(x) + \frac{1}{(x^{7} + 7)(x)} - 7x^{6}ln(x) - \frac{x^{7}}{(x)} + \frac{1}{7}*7x^{6}\\=&\frac{-7x^{6}ln(x)}{(x^{7} + 7)^{2}} + \frac{1}{(x^{7} + 7)x} - 7x^{6}ln(x)\\ \end{split}\end{equation} \]

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