There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + 2)}^{3}sqrt(3 - x){\frac{1}{(x + 1)}}^{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}sqrt(-x + 3)}{(x + 1)^{5}} + \frac{6x^{2}sqrt(-x + 3)}{(x + 1)^{5}} + \frac{12xsqrt(-x + 3)}{(x + 1)^{5}} + \frac{8sqrt(-x + 3)}{(x + 1)^{5}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}sqrt(-x + 3)}{(x + 1)^{5}} + \frac{6x^{2}sqrt(-x + 3)}{(x + 1)^{5}} + \frac{12xsqrt(-x + 3)}{(x + 1)^{5}} + \frac{8sqrt(-x + 3)}{(x + 1)^{5}}\right)}{dx}\\=&(\frac{-5(1 + 0)}{(x + 1)^{6}})x^{3}sqrt(-x + 3) + \frac{3x^{2}sqrt(-x + 3)}{(x + 1)^{5}} + \frac{x^{3}(-1 + 0)*\frac{1}{2}}{(x + 1)^{5}(-x + 3)^{\frac{1}{2}}} + 6(\frac{-5(1 + 0)}{(x + 1)^{6}})x^{2}sqrt(-x + 3) + \frac{6*2xsqrt(-x + 3)}{(x + 1)^{5}} + \frac{6x^{2}(-1 + 0)*\frac{1}{2}}{(x + 1)^{5}(-x + 3)^{\frac{1}{2}}} + 12(\frac{-5(1 + 0)}{(x + 1)^{6}})xsqrt(-x + 3) + \frac{12sqrt(-x + 3)}{(x + 1)^{5}} + \frac{12x(-1 + 0)*\frac{1}{2}}{(x + 1)^{5}(-x + 3)^{\frac{1}{2}}} + 8(\frac{-5(1 + 0)}{(x + 1)^{6}})sqrt(-x + 3) + \frac{8(-1 + 0)*\frac{1}{2}}{(x + 1)^{5}(-x + 3)^{\frac{1}{2}}}\\=&\frac{-5x^{3}sqrt(-x + 3)}{(x + 1)^{6}} + \frac{3x^{2}sqrt(-x + 3)}{(x + 1)^{5}} - \frac{x^{3}}{2(x + 1)^{5}(-x + 3)^{\frac{1}{2}}} - \frac{30x^{2}sqrt(-x + 3)}{(x + 1)^{6}} + \frac{12xsqrt(-x + 3)}{(x + 1)^{5}} - \frac{3x^{2}}{(x + 1)^{5}(-x + 3)^{\frac{1}{2}}} - \frac{60xsqrt(-x + 3)}{(x + 1)^{6}} + \frac{12sqrt(-x + 3)}{(x + 1)^{5}} - \frac{6x}{(x + 1)^{5}(-x + 3)^{\frac{1}{2}}} - \frac{40sqrt(-x + 3)}{(x + 1)^{6}} - \frac{4}{(x + 1)^{5}(-x + 3)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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