There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(x + 2){(3 - x)}^{4}{\frac{1}{(x + 1)}}^{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{4}sqrt(x + 2)}{(x + 1)^{5}} - \frac{12x^{3}sqrt(x + 2)}{(x + 1)^{5}} + \frac{54x^{2}sqrt(x + 2)}{(x + 1)^{5}} - \frac{108xsqrt(x + 2)}{(x + 1)^{5}} + \frac{81sqrt(x + 2)}{(x + 1)^{5}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{4}sqrt(x + 2)}{(x + 1)^{5}} - \frac{12x^{3}sqrt(x + 2)}{(x + 1)^{5}} + \frac{54x^{2}sqrt(x + 2)}{(x + 1)^{5}} - \frac{108xsqrt(x + 2)}{(x + 1)^{5}} + \frac{81sqrt(x + 2)}{(x + 1)^{5}}\right)}{dx}\\=&(\frac{-5(1 + 0)}{(x + 1)^{6}})x^{4}sqrt(x + 2) + \frac{4x^{3}sqrt(x + 2)}{(x + 1)^{5}} + \frac{x^{4}(1 + 0)*\frac{1}{2}}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}} - 12(\frac{-5(1 + 0)}{(x + 1)^{6}})x^{3}sqrt(x + 2) - \frac{12*3x^{2}sqrt(x + 2)}{(x + 1)^{5}} - \frac{12x^{3}(1 + 0)*\frac{1}{2}}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}} + 54(\frac{-5(1 + 0)}{(x + 1)^{6}})x^{2}sqrt(x + 2) + \frac{54*2xsqrt(x + 2)}{(x + 1)^{5}} + \frac{54x^{2}(1 + 0)*\frac{1}{2}}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}} - 108(\frac{-5(1 + 0)}{(x + 1)^{6}})xsqrt(x + 2) - \frac{108sqrt(x + 2)}{(x + 1)^{5}} - \frac{108x(1 + 0)*\frac{1}{2}}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}} + 81(\frac{-5(1 + 0)}{(x + 1)^{6}})sqrt(x + 2) + \frac{81(1 + 0)*\frac{1}{2}}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}}\\=&\frac{-5x^{4}sqrt(x + 2)}{(x + 1)^{6}} + \frac{4x^{3}sqrt(x + 2)}{(x + 1)^{5}} + \frac{x^{4}}{2(x + 1)^{5}(x + 2)^{\frac{1}{2}}} + \frac{60x^{3}sqrt(x + 2)}{(x + 1)^{6}} - \frac{36x^{2}sqrt(x + 2)}{(x + 1)^{5}} - \frac{6x^{3}}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}} - \frac{270x^{2}sqrt(x + 2)}{(x + 1)^{6}} + \frac{108xsqrt(x + 2)}{(x + 1)^{5}} + \frac{27x^{2}}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}} + \frac{540xsqrt(x + 2)}{(x + 1)^{6}} - \frac{108sqrt(x + 2)}{(x + 1)^{5}} - \frac{54x}{(x + 1)^{5}(x + 2)^{\frac{1}{2}}} - \frac{405sqrt(x + 2)}{(x + 1)^{6}} + \frac{81}{2(x + 1)^{5}(x + 2)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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