There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(x + 1)}^{2}){(3 - x)}^{3}}{sqrt(x + 3)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-x^{5}}{sqrt(x + 3)} + \frac{7x^{4}}{sqrt(x + 3)} - \frac{10x^{3}}{sqrt(x + 3)} - \frac{18x^{2}}{sqrt(x + 3)} + \frac{27x}{sqrt(x + 3)} + \frac{27}{sqrt(x + 3)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-x^{5}}{sqrt(x + 3)} + \frac{7x^{4}}{sqrt(x + 3)} - \frac{10x^{3}}{sqrt(x + 3)} - \frac{18x^{2}}{sqrt(x + 3)} + \frac{27x}{sqrt(x + 3)} + \frac{27}{sqrt(x + 3)}\right)}{dx}\\=&\frac{-5x^{4}}{sqrt(x + 3)} - \frac{x^{5}*-(1 + 0)*\frac{1}{2}}{(x + 3)(x + 3)^{\frac{1}{2}}} + \frac{7*4x^{3}}{sqrt(x + 3)} + \frac{7x^{4}*-(1 + 0)*\frac{1}{2}}{(x + 3)(x + 3)^{\frac{1}{2}}} - \frac{10*3x^{2}}{sqrt(x + 3)} - \frac{10x^{3}*-(1 + 0)*\frac{1}{2}}{(x + 3)(x + 3)^{\frac{1}{2}}} - \frac{18*2x}{sqrt(x + 3)} - \frac{18x^{2}*-(1 + 0)*\frac{1}{2}}{(x + 3)(x + 3)^{\frac{1}{2}}} + \frac{27}{sqrt(x + 3)} + \frac{27x*-(1 + 0)*\frac{1}{2}}{(x + 3)(x + 3)^{\frac{1}{2}}} + \frac{27*-(1 + 0)*\frac{1}{2}}{(x + 3)(x + 3)^{\frac{1}{2}}}\\=&\frac{-5x^{4}}{sqrt(x + 3)} + \frac{x^{5}}{2(x + 3)^{\frac{3}{2}}} + \frac{28x^{3}}{sqrt(x + 3)} - \frac{7x^{4}}{2(x + 3)^{\frac{3}{2}}} - \frac{30x^{2}}{sqrt(x + 3)} + \frac{5x^{3}}{(x + 3)^{\frac{3}{2}}} - \frac{36x}{sqrt(x + 3)} + \frac{9x^{2}}{(x + 3)^{\frac{3}{2}}} + \frac{27}{sqrt(x + 3)} - \frac{27x}{2(x + 3)^{\frac{3}{2}}} - \frac{27}{2(x + 3)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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