There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(x + 1)}{((30 + x)(29 + x)(28 + x)(27 + x)(26 + x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)} + \frac{1}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)} + \frac{1}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)}\right)}{dx}\\=&(\frac{-(3061524 + 219100*2x + 7835*3x^{2} + 5x^{4} + 140*4x^{3} + 0)}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}})x + \frac{1}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)} + (\frac{-(3061524 + 219100*2x + 7835*3x^{2} + 5x^{4} + 140*4x^{3} + 0)}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}})\\=& - \frac{461705x^{2}}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}} - \frac{24065x^{3}}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}} - \frac{5x^{5}}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}} - \frac{565x^{4}}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}} - \frac{3499724x}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}} + \frac{1}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)} - \frac{3061524}{(3061524x + 219100x^{2} + 7835x^{3} + x^{5} + 140x^{4} + 17100720)^{2}}\\ \end{split}\end{equation} \]

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