There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ log_{2}^{\frac{({(x - 2)}^{5})}{({(x + 3)}^{2})}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = log_{2}^{\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{2}^{\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}}}\right)}{dx}\\=&(\frac{(\frac{((\frac{-2(1 + 0)}{(x + 3)^{3}})x^{5} + \frac{5x^{4}}{(x + 3)^{2}} - 10(\frac{-2(1 + 0)}{(x + 3)^{3}})x^{4} - \frac{10*4x^{3}}{(x + 3)^{2}} + 40(\frac{-2(1 + 0)}{(x + 3)^{3}})x^{3} + \frac{40*3x^{2}}{(x + 3)^{2}} - 80(\frac{-2(1 + 0)}{(x + 3)^{3}})x^{2} - \frac{80*2x}{(x + 3)^{2}} + 80(\frac{-2(1 + 0)}{(x + 3)^{3}})x + \frac{80}{(x + 3)^{2}} - 32(\frac{-2(1 + 0)}{(x + 3)^{3}}))}{(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})} - \frac{(0)log_{2}^{\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}}}}{(2)})}{(ln(2))})\\=&\frac{-2x^{5}}{(x + 3)^{3}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} + \frac{5x^{4}}{(x + 3)^{2}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} + \frac{20x^{4}}{(x + 3)^{3}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} - \frac{40x^{3}}{(x + 3)^{2}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} - \frac{80x^{3}}{(x + 3)^{3}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} + \frac{120x^{2}}{(x + 3)^{2}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} + \frac{160x^{2}}{(x + 3)^{3}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} - \frac{160x}{(x + 3)^{2}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} - \frac{160x}{(x + 3)^{3}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} + \frac{80}{(x + 3)^{2}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)} + \frac{64}{(x + 3)^{3}(\frac{x^{5}}{(x + 3)^{2}} - \frac{10x^{4}}{(x + 3)^{2}} + \frac{40x^{3}}{(x + 3)^{2}} - \frac{80x^{2}}{(x + 3)^{2}} + \frac{80x}{(x + 3)^{2}} - \frac{32}{(x + 3)^{2}})ln(2)}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！