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

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