There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{log_{2}^{{(x - 2)}^{5}}}{({(x + 3)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{log_{2}^{x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32}}{(x + 3)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{log_{2}^{x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32}}{(x + 3)^{2}}\right)}{dx}\\=&(\frac{-2(1 + 0)}{(x + 3)^{3}})log_{2}^{x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32} + \frac{(\frac{(\frac{(5x^{4} - 10*4x^{3} + 40*3x^{2} - 80*2x + 80 + 0)}{(x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32)} - \frac{(0)log_{2}^{x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32}}{(2)})}{(ln(2))})}{(x + 3)^{2}}\\=&\frac{-2log_{2}^{x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32}}{(x + 3)^{3}} + \frac{5x^{4}}{(x + 3)^{2}(x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32)ln(2)} - \frac{40x^{3}}{(x + 3)^{2}(x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32)ln(2)} + \frac{120x^{2}}{(x + 3)^{2}(x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32)ln(2)} - \frac{160x}{(x + 3)^{2}(x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32)ln(2)} + \frac{80}{(x + 3)^{2}(x^{5} - 10x^{4} + 40x^{3} - 80x^{2} + 80x - 32)ln(2)}\\ \end{split}\end{equation} \]

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